The plaintiffs appeal several determinations of the United States District Court for the Southern District of New York (Buchwald, District Judge). The plaintiffs raise the following issues: (1) whether their state-law claims for recovery of prevailing wages and overtime pay should have been dismissed; (2) whether the plaintiffs should have been permitted to amend their complaint to add a claim under Article 6 of New York’s Labor Law; (3) whether their FLSA claims for unpaid overtime compensation should have been limited to one-and-a-half times the hourly rates actually paid, rather than one-and-a-half times the prevailing hourly rates; and (4) whether the district court should have directed a verdict against the four non-testifying plaintiffs.
For the reasons that follow, we affirm each of the district court’s determinations.
BACKGROUND
The appellants are nine plaintiffs who were employed as roofers and bricklayers on three separate public works construction projects. The defendants-appellees are contractors involved in these projects, their officers, and the insurance companies that served as sureties on construction payment bonds for those projects.
The contractor defendants are Ypsilon Construction Corporation, Inc. (“Ypsilon”), Phoenix Construction Corporation (“Phoenix”) and Ajet Construction Corporation (“Ajet”). All three are construction companies.
The insurance defendants are Republic Western Insurance Company (“Republic”), Utica Mutual Insurance Company (“Uti-ca”) and International Fidelity Insurance Company (“IFIC”). All three companies are sureties on construction payment bonds.
Three construction projects are involved and each contract involves the New York City Housing Authority (“NYCHA”) as owner 'of three public housing developments — the Fulton Houses, the Lillian Wald Houses and the Queensbridge Houses.
NYCHA hired Ypsilon to perform exterior brick repair at' the Fulton Houses (the “Fulton Project”), Phoenix to perform asbestos abatement and roofing renovations on' the Lillian Wald Houses (the “Wald Project”), and Phoenix and Ajet, as a joint venture (the “Joint Venture”), to perform roofing renovations, asbestos abatement and brickwork repair at the Queensbridge Houses (the “Queensbridge Project”). All three NYCHA projects were federally funded.
Each project, of course, was subject to a separate contract but all contract provisions relevant to this appeal were identical. The General Conditions bf each contract required that workers on the projects be paid wage rates and supplemental fringe benefits prevailing at the time the work was performed. The General Conditions of each contract stated that the Davis-Bacon Act, 40 U.S.C. § 276a, et seq. (“DBA”), and the Contract Work Hours and Safety Standards Act, 40 U.S.C. § 327, et seq. (“CWHASSA”), were specific labor standards provisions applicable to all federally funded contracts. Section 42(a) of the General Conditions provided that “[t]he Contractor shall pay to all laborers and mechanics employed in the work not less than the wages prevailing in the locality of the Project, as predetermined' by the Secretary of Labor of the United States pursuant to the Davis-Bacon Act (Title 40, U.S.C., Sections 276a—276a-5).”
The plaintiffs sued in the United States District Court for the Southern District of New York (Kaplan, District Judge) to re*84cover unpaid prevailing wages and overtime compensation allegedly owed them for their labor on all three projects. The plaintiffs invoked the Fair Labor Standards Act, 29 U.S.C. § 201, et seq. (the “FLSA”), the CWHASSA and New York State common law.
The district court issued a scheduling order setting the deadline for reply on all pleadings for late December 1997. The pretrial order was filed in June 1998. On consent of the parties, the case was transferred to then Magistrate Judge Buchwald for all pretrial purposes.
Several defendants moved to dismiss for failure to state a claim, while others moved for summary judgment. Immediately following oral argument on April 17, 1999, Magistrate Judge Buchwald dismissed the plaintiffs’ CWHASSA claims, holding that the statute does not create a private right of action. The district court also dismissed the plaintiffs’ state-law claims because state common law remedies are not available to recover prevailing wages under the federally funded contracts. The district court also held that the DBA, the statute applicable to federal contracts, does not afford the plaintiffs a private right of action.
The plaintiffs requested reconsideration of the district court’s dismissal of their state-law claims and also moved to amend their complaint to add a claim under Article 6 of the New York Labor Law. The district court denied reconsideration as well as the plaintiffs’ motion to amend the complaint, citing the plaintiffs’ undue delay in bringing the motion. Grochowski v. Ajet Construction Corp., 1999 WL 688450, *1 (S.D.N.Y. Sept.2, 1999).
Subsequently, in response to additional motions by several defendants for summary judgment, now District Judge Buchwald pared the plaintiffs’ claims down to one remedy: the unpaid minimum wages, if any, and unpaid overtime in the amount of one and one-half times the hourly rates actually paid. Grochowski v. Ajet Construction Corp., 2000 WL 1159640 (S.D.N.Y. Aug.16, 2000). The case went to a jury trial on the limited issues of minimum wages and time-and-a-half for overtime under the FLSA.
The claims of only five of the original nine plaintiffs were submitted to the jury. Two of the plaintiffs who lived in New York chose not to appear at trial. Two other plaintiffs lived in Poland and did not return to the United States. Plaintiffs’ counsel did not take their depositions, despite the opportunity to do so via telephone shortly before trial. After the plaintiffs rested at trial, the district court granted judgment as a matter of law against the four non-testifying plaintiffs on the ground that they failed to present sufficient evidence for the jury to make a reasonable inference as to the hours worked or wages paid.
The jury awarded each of the five remaining plaintiffs approximately $26,-000.00 — double the unpaid wages of $13,000.00 because of the defendants’ willful conduct, a sanction permitted under the FLSA. 29 U.S.C. § 216(b).
The plaintiffs make the following claims on appeal: (1) their state-law claims should not have been dismissed; (2) the plaintiffs should have been permitted to amend their complaint; (3) their FLSA claims should not have been limited to one- and-a-half times the hourly rates actually paid; and (4) judgment as a matter of law was improperly entered against the four non-testifying plaintiffs.
DISCUSSION
I. State Comrmn-Law Claims
The plaintiffs’ state-law claims for breach of contract and quantum meruit *85were dismissed on summary judgment. Thus, we review this issue de novo to determine whether the substantive law has been correctly applied. Republic Nat’l Bank of New York v. Delta Air Lines, 263 F.3d 42, 46 (2d Cir.2001).
The construction projects were federally funded and the contracts specifically provided that the DBA applied. The DBA requires that all laborers and mechanics working on federally funded construction projects be paid not less than the prevailing wage in the locality where the work is performed. 40 U.S.C. § 276a. Although the Supreme Court has not considered whether the DBA confers a private right of action on an aggrieved employee for back wages, the great weight of authority indicates that it does not. See, e.g., Operating Eng’rs Health & Welfare Trust Fund v. JWJ Contracting Co., 135 F.3d 671, 676 (9th Cir.1998); Chan v. City of New York, 1 F.3d 96, 102 (2d Cir.1993); Weber v. Heat Control Co., 728 F.2d 599, 599-600 (3d Cir.1984).
In Chan v. City of New York, 1 F.3d 96 (2d Cir.1993), this Court indicated that a private right of action does not exist under the DBA. Id. at 102. In Chan, laborers under municipal contracts sued the contractor, the City of New York and the New York City Department of Housing Preservation and Development for back wages alleging that they were not paid prevailing wages as required — not by the DBA — but by the Housing Community and Development Act (“HCDA”). Id. at 99.
In determining that no private right of action exists under HCDA, we found an analogy in Congress’ adoption of the DBA’s regulatory scheme providing administrative remedies. Id. at 102. The Court determined that, although there is no statement that the administrative remedies are exclusive, there is simply no indication that, along with the cited regulatory mechanism, Congress intended to authorize private suits. Id
It is an “elemental canon” of statutory construction that where a statute expressly provides a remedy, “courts must be especially reluctant to provide additional remedies.” Karahalios v. Nat’l Fed’n of Employees, Local 1263, 489 U.S. 527, 533, 109 S.Ct. 1282, 103 L.Ed.2d 539 (1989) (citing Transamerica Mortgage Advisors, Inc. v. Lewis, 444 U.S. 11, 19, 100 S.Ct. 242, 62 L.Ed.2d 146 (1979)). In such cases, “[i]n the absence of strong indicia of contrary congressional intent, we are compelled to conclude that Congress provided precisely the remedies it considered appropriate.” Id (quoting Middlesex County Sewerage Auth. v. Nat’l Sea Clammers Ass’n, 453 U.S. 1, 15, 101 S.Ct. 2615, 69 L.Ed.2d 435 (1981)) (internal quotation marks omitted).
Although the Court in Chan found that a civil rights action for the violation of the minimum wage provision was available under 42 U.S.C. § 1983, the Court differentiated between a private right of action conferred by statute and an action under § 1983. Id. at 103. The Court noted “the § 1983 inquiry begins with a presumption in favor of the right to bring suit, for the ‘general rule’ is that § 1983 provides a remedy for violations of federal statutory rights unless ‘Congress has affirmatively withdrawn the remedy.’ ” Id. (quoting Wilder v. Virginia Hosp. Ass’n, 496 U.S. 498, 509 n. 9, 110 S.Ct. 2510, 110 L.Ed.2d 455 (1990)).
Here, the plaintiffs did not bring a § 1983 action. Nor did they allege claims directly under the DBA, but instead brought state-law claims for breach of contract as third party beneficiaries of the contracts and for quantum meruit. Unlike claims brought under § 1983, there is no *86presumption in favor of a right to bring suit for such common law claims.
At bottom, the plaintiffs’ state-law claims are indirect attempts at privately enforcing the prevailing wage schedules contained in the DBA. To allow a third-party private contract action aimed at enforcing those wage schedules would be “inconsistent with the underlying purpose of the legislative scheme and would interfere with the implementation of that scheme to the same extent as would a cause of action directly under the statute.” Davis v. United Air Lines, Inc., 575 F.Supp. 677, 680 (E.D.N.Y.1983) (internal quotation marks omitted) (rejecting common law contract claim as “end-run” around statute on remand after this Court held the Vocational Rehabilitation Act provided no private right of action).
The plaintiffs rely almost exclusively on the New York Court of Appeals case of Fata v. S.A. Healy Co., 289 N.Y. 401, 46 N.E.2d 339 (1943), for the proposition that, consistent with § 220 of the New York Labor Law employees can bring parallel actions seeking recovery of wages both under an administrative structure and through common-law remedies. However, the present contracts between the defendants and the NYCHA were federally funded and, as such, are governed by the prevailing wage requirements set forth in the DBA, not by § 220 of the New York Labor Law. Since in this case, unlike in Fata, no private right of action exists under the relevant statute, the plaintiffs efforts to bring their claims as state common-law claims are clearly an impermissible “end run” around the DBA.
II. Denial of Leave to Amend
The plaintiffs also appeal the district court’s denial of their letter motion to amend the complaint to add a claim under Article 6 of the New York Labor Law.
We review a district court’s decision to grant or deny a party leave to amend a pleading under Federal Rule of Civil Procedure 15(a) for abuse of discretion. Block v. First Blood Assocs., 988 F.2d 344, 350 (2d Cir.1993). Similarly, a scheduling order ruling under Federal Rule of Civil Procedure 16(b) is also reviewed for abuse of discretion. Parker v. Columbia Pictures Indus., 204 F.3d 326, 339 (2d Cir.2000).
Where a scheduling order has been entered, the lenient standard under Rule 15(a), which provides leave to amend “shall be freely given,” must be balanced against the requirement under Rule 16(b) that the Court’s scheduling order “shall not be modified except upon a showing of good cause.” Fed.R.Civ.P. 15(a), 16(b). A finding of good cause depends on the diligence of the moving party. Parker, 204 F.3d at 340 (citing In re Milk Prods. Antitrust Litig., 195 F.3d 430, 437 (8th Cir.1999)).
The district court issued a scheduling order setting December 24, 1997 as the deadline for reply on all pleadings. The pretrial order was filed on June 1, 1998. The plaintiffs moved to amend their complaint in August 1999 based on the June 2, 1998 decision of the New York State Appellate Division in Pesantez v. Boyle Envtl. Servs., 251 A.D.2d 11, 673 N.Y.S.2d 659 (1st Dep’t 1998). The plaintiffs delayed more than one year before seeking to amend their complaint. Furthermore, when the motion was filed, discovery had been completed and a summary judgment motion was pending. On this record we cannot say that the district court abused its discretion in denying the plaintiffs’ motion to amend.
III. Calculation of FLSA Overtime Compensation
The plaintiffs’ challenge to the district court’s calculation of the plaintiffs’ *87FLSA claims for overtime compensation raises a question of statutory interpretation, which we review de novo. Goodrich Corp. v. Town of Middlebury, 311 F.3d 154, 177 (2d Cir.2002).
The plaintiffs contend that, under both the DBA and the contract between the defendants and NYCHA, their overtime compensation should have been calculated at time-and-a-half the prevailing hourly rates, rather than at time-and-a-half the hourly rates the plaintiffs were actually paid. Although the plaintiffs brought this claim under the FLSA, not the DBA, they now wish to apply the more generous prevailing wage structure of the DBA to their claim for unpaid overtime compensation.
The FLSA, however, serves a different purpose than the DBA. The DBA provides for the payment of locally prevailing wages for work on federally funded projects. 40 U.S.C. § 276a; see Universities Research Ass’n v. Coutu, 450 U.S. 754, 773-74, 101 S.Ct. 1451, 67 L.Ed.2d 662 (1981). In contrast, the FLSA requires employers to pay each employee a guaranteed minimum wage, and it does not address liability for underpayment of hours at prevailing wage rates. 29 U.S.C. § 206(a)(1).
Under the FLSA, employees may recover unpaid overtime compensation and an additional amount of liquidated damages. 29 U.S.C. § 216(b). The FLSA requires that employees be paid overtime compensation equal to at least “one and one-half times the regular rate at which [the employee] is employed,” for all hours worked in excess of forty per week. 29 U.S.C. § 207(a)(1). Although the FLSA does not expressly define “regular rate” of pay, the Supreme Court has determined that it is “the hourly rate actually paid the employee for the normal, non-overtime workweek for which he is employed.” Walling v. Youngerman-Reynolds Hardwood Co., 325 U.S. 419, 424, 65 S.Ct. 1242, 89 L.Ed. 1705 (1945) (citation omitted) (emphasis added).
Under the DBA, an aggrieved employee is limited to those administrative mechanisms set forth in the text of the statute. Chan, 1 F.3d at 102. The plaintiffs’ attempt to use the FLSA to circumvent the procedural requirements of the DBA must fail. The plaintiffs’ forum for determining prevailing wages is the NY-CHA, which can consider all aspects of the plaintiffs’ wages and hours and compute underpayment for overtime hours at one- and-a-half times the prevailing wage. Grochowski, 2000 WL 1159640, at *4.
For the foregoing reasons, the district court properly limited the plaintiffs’ claims under the FLSA for unpaid overtime compensation to one-and-a-half times the hourly rates actually paid.
IV. Directed Verdict Against Non-Appearing Plaintiffs
The plaintiffs assert that the district court erred in directing a verdict against the four non-testifying plaintiffs. This Court reviews a district court’s grant of judgment as a matter of law de novo, and we apply the same standard the district court was required to apply. Diesel v. Town of Lewisboro, 232 F.3d 92, 103 (2d Cir.2000).
An employee who sues for unpaid minimum wages or overtime compensation has the burden of proving that the employer did not compensate him for completed work. Anderson v. Mt. Clemens Pottery Co., 328 U.S. 680, 686-87, 66 S.Ct. 1187, 90 L.Ed. 1515 (1946). Under the FLSA, even “[w]hen accurate records or precise evidence of the hours worked do not exist, ‘an employee has carried out his burden if he proves that he has in fact performed work for which he was improp*88erly compensated and if he produces sufficient evidence to show the amount and extent of that work as a matter of just and reasonable inference.’ ” Tran v. Alphonse Hotel Corp., 281 F.3d 23, 31 (2d Cir.2002) (quoting Anderson, 328 U.S. at 687, 66 S.Ct. 1187). Although the plaintiffs correctly point out that not all employees need testify in order to prove FLSA violations or recoup back-wages, the plaintiffs must present sufficient evidence for the jury to make a reasonable inference as to the number of hours worked by the non-testifying employees. Herman v. Hector I. Nieves Transport, Inc., 91 F.Supp.2d 435, 446 (D.P.R.2000).
Andrzej Wiktoruk, Andrzej Zmijewski, Jerzy Klosek and Miroslav Sidor failed to submit any evidence whatsoever on their behalf. Wiktoruk and Zmijewski chose not to testify. Klosek and Sidor were residing in Poland at the time of the trial and declined to sit for depositions. Instead, these four plaintiffs relied on bits of testimony from various co-plaintiffs.
A.Wiktoruk
With regard to Wiktoruk, plaintiff Jan Statkiweicz testified that Wiktoruk worked on the Fulton project, and that a standard work day at the site was eight hours. Janusz Wysocki also testified that Wikto-ruk worked as a mason on the Fulton project, but did not specify Wiktoruk’s hours or rate of pay. Likewise, Henryk Supinski testified that Wiktoruk worked on the Fulton project in 1994 and 1995, but did not supply any details about Wikto-ruk’s hours or pay. Ramon Kakol testified that Wiktoruk worked on the Wald project, but could not recall whether Wiktoruk worked with him the entire time Kakol worked there. Thus, there was no evidence establishing how many hours Wikto-ruk worked on the Fulton and Wald projects or his rate of pay.
B. Zmijewski
To establish the hours worked and rate paid to Zmijewski, the plaintiffs rely on Statkiweicz, who testified that he “usually” worked with Zmijewski at the Fulton project, and that both worked “[b]asieally the same” hours from April to December 1994. In addition, Zmijewski’s calendar was introduced to establish his hours in 1995. We note, however, that the plaintiffs fail to point to evidence of Zmijewski’s rate of pay in their appellate briefs.
C. Klosek
Statkiweicz and Wysocki testified that they worked with Klosek on the Fulton project. Statkiweicz stated that he worked on Saturdays with Klosek, but did not know if he worked on all Saturdays with Klosek “because people rotated.” Wysocki did not indicate what days he may have worked with Klosek. As such, the jury could have no reasonable basis to determine how many hours Klosek worked or how much he was paid.
D. Sidor
Finally, Wysocki testified that Sidor worked with him on the Wald, Futon and Queensbridge projects and that Sidor was his roofing partner on the Wald project. Wysocki also testified that Sidor was not paid more than nine dollars per hour. Although the evidence established what Si-dor was not paid, there was no evidence establishing what he was paid. Furthermore, the plaintiffs adduced little evidence that would allow the jury to draw a reasonable inference about how many hours Sidor worked.
The corpus of evidence on behalf of the foregoing four plaintiffs was simply inadequate for a jury to determine whether their claims had any merit. Notably, none of the non-testifying plaintiffs point to any *89evidence establishing the amounts they were paid. In addition, there is only speculation to establish what hours these plaintiffs worked. Accordingly, the district court correctly granted the defendants’ motion for judgment as a matter of law against the four non-testifying plaintiffs.
CONCLUSION
For the reasons stated herein, we AFFIRM the judgment of the district court.