ARNOLD, Circuit Judge.
The plaintiffs are current and former firefighters for the City of Aberdeen, South Dakota, who have sued the City to recover overtime pay that they claim is due them under the Fair Labor Standards Act (FLSA). Both sides agreed that no facts were in dispute and moved for summary judgment. The district court denied the plaintiffs’ motion for partial summary judgment but granted judgment to the City, concluding that the FLSA’s plain language prevents the payment of overtime wages to those who have not actually worked. We review the district court’s grant of a motion for summary judgment de novo. Woods v. DaimlerChrysler Corp., 409 F.3d 984, 990 (8th Cir.2005). Because the relevant facts are not in dispute and the judgment is final, we also review the court’s denial of the plaintiffs motion for partial summary judgment de novo.' See White Consol. Indus., Inc. v. McGill Mfg. Co., 165 F.3d 1185, 1190 (8th Cir.1999). After careful consideration, we reverse.
The plaintiffs were often scheduled to work more hours than the FLSA permits [672]*672an employee to work without receiving overtime pay, and on some of those occasions the plaintiffs would ask other employees to work shifts on their behalf. This kind of arrangement is common among firefighters and is permissible under the FLSA so long as it is voluntary and done with the employer’s permission. 29 U.S.C. § 207(p)(3). When a substitution occurs, the employer pays the scheduled employee and not the substitute; the amount that the substitute receives is fixed by private agreement between the two employees. The City paid the plaintiffs straight time for their substituted shifts and also credited them for the purposes of seniority and leave time, but it refused to pay them the overtime to which the FLSA plainly would have entitled them had they worked the shifts themselves. The plaintiffs contend that a federal regulation entitled them to the same amount of overtime pay when substitutes worked their shifts for them.
When a public employee works a shift for another employee, the law provides that “the hours such employee worked as a substitute shall be excluded by the public agency in the calculation of the hours for which the employee is entitled to overtime compensation, under this section.” 29 U.S.C. § 207(p)(3). A brief example may help: Imagine two employees who are each scheduled to work forty-four hours one week. Employee A works thirty-six hours and asks employee B to work the last eight-hour shift on her behalf. Employee B agrees and works the shift. Even though employee B worked fifty-two hours that week, he is paid for only forty-four hours and receives only four hours of overtime pay. (As we have said, the compensation that employee B receives for the additional eight hours is determined by agreement between employees A and B.)
The parties concede this but disagree on whether the employer in our example has to pay four hours of overtime pay to employee A. The Department of Labor has promulgated a regulation stating that when one employee substitutes for another the hours worked are “excluded” from the hours “for which the substituting employee would otherwise be entitled to overtime compensation,” and “each employee will be credited as if he or she had worked his or her normal work schedule for that shift.” 29 C.F.R. § 553.31(a). The plaintiffs read this regulation as requiring the City to pay overtime wages to the scheduled employee. The City contends that the regulation is void because a statute governing overtime, 29 U.S.C. § 207(a)(1), requires that a person actually work more than the statutory maximum number of hours to receive overtime pay.
When reviewing an agency’s construction of a statute, we look first to whether the statute’s language and legislative history clearly demonstrate what Congress intended. North Dakota ex rel. Olson v. Centers for Medicare & Medicaid Sens., 403 F.3d 537, 539 (8th Cir.2005). When they do, that intent controls and a court will not defer to any regulation that interprets the statute in a contrary manner. Id; see also Chevron U.S.A., Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 843, 845, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984). But when Congress’s intent is unclear and the statute contains an explicit or implicit gap, we will defer to the agency’s regulation so long as it is not “arbitrary, capricious, or manifestly contrary to the statute.” Id. at 844, 104 S.Ct. 2778; Friends of the Boundary Waters Wilderness v. Bosworth, 437 F.3d 815, 821-22 (8th Cir.2006).
In support of its plain-language argument, the City cites to language in the FLSA that says “no employer shall employ [673]*673any of his employees who in any workweek is engaged in commerce or in the production of goods for commerce, or is employed in an enterprise engaged in commerce or in the production of goods for commerce, for. a workweek longer than forty hours unless such employee receives [overtime wages].” 29 U.S.C. § 207(a)(1) (emphasis added). This language, the City says, means that the employee must be engaged (i.e., actively working) to receive overtime wages. But a more careful parsing of the section reveals that the statute uses the phrase “engaged in commerce” as a kind of applicational threshold: The overtime provisions of § 207(a) apply if the employee is engaged in commerce or in the production of goods for commerce at any time during the work week. And even if the employee is not engaged in commerce or in the production of goods for commerce, § 207(a) applies if the “enterprise” for which he or she works is so engaged. Id. The word “engaged” therefore relates not to whether the employee was actively working, but whether the employee’s or enterprise’s work was of a certain kind.
We question, moreover, the applicability of § 207(a) to these current and former firefighters. Congress amended the FLSA in 1974 so that its provisions would apply to state and local employees. In the course of passing those amendments, the House and Senate agreed to a partial exemption to the overtime rules for firefighters and police officers. Section 207(k) of the FLSA reflects that compromise. Under that provision, state and local employers of firefighters are not bound to the seven-day work period in 207(a), but may instead extend the relevant work period to as long as 28 days. 29 U.S.C. § 207(k). In addition, an employer must pay overtime wages only if a firefighter’s total “tours of duty” exceed 212 hours in a 28-day work period; for shorter work periods, the ratio of 212 to 28 is used to compute how many hours must be in a firefighter’s total “tours of duty” before he or she is entitled to overtime pay. Id.; 29 C.F.R.
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ARNOLD, Circuit Judge.
The plaintiffs are current and former firefighters for the City of Aberdeen, South Dakota, who have sued the City to recover overtime pay that they claim is due them under the Fair Labor Standards Act (FLSA). Both sides agreed that no facts were in dispute and moved for summary judgment. The district court denied the plaintiffs’ motion for partial summary judgment but granted judgment to the City, concluding that the FLSA’s plain language prevents the payment of overtime wages to those who have not actually worked. We review the district court’s grant of a motion for summary judgment de novo. Woods v. DaimlerChrysler Corp., 409 F.3d 984, 990 (8th Cir.2005). Because the relevant facts are not in dispute and the judgment is final, we also review the court’s denial of the plaintiffs motion for partial summary judgment de novo.' See White Consol. Indus., Inc. v. McGill Mfg. Co., 165 F.3d 1185, 1190 (8th Cir.1999). After careful consideration, we reverse.
The plaintiffs were often scheduled to work more hours than the FLSA permits [672]*672an employee to work without receiving overtime pay, and on some of those occasions the plaintiffs would ask other employees to work shifts on their behalf. This kind of arrangement is common among firefighters and is permissible under the FLSA so long as it is voluntary and done with the employer’s permission. 29 U.S.C. § 207(p)(3). When a substitution occurs, the employer pays the scheduled employee and not the substitute; the amount that the substitute receives is fixed by private agreement between the two employees. The City paid the plaintiffs straight time for their substituted shifts and also credited them for the purposes of seniority and leave time, but it refused to pay them the overtime to which the FLSA plainly would have entitled them had they worked the shifts themselves. The plaintiffs contend that a federal regulation entitled them to the same amount of overtime pay when substitutes worked their shifts for them.
When a public employee works a shift for another employee, the law provides that “the hours such employee worked as a substitute shall be excluded by the public agency in the calculation of the hours for which the employee is entitled to overtime compensation, under this section.” 29 U.S.C. § 207(p)(3). A brief example may help: Imagine two employees who are each scheduled to work forty-four hours one week. Employee A works thirty-six hours and asks employee B to work the last eight-hour shift on her behalf. Employee B agrees and works the shift. Even though employee B worked fifty-two hours that week, he is paid for only forty-four hours and receives only four hours of overtime pay. (As we have said, the compensation that employee B receives for the additional eight hours is determined by agreement between employees A and B.)
The parties concede this but disagree on whether the employer in our example has to pay four hours of overtime pay to employee A. The Department of Labor has promulgated a regulation stating that when one employee substitutes for another the hours worked are “excluded” from the hours “for which the substituting employee would otherwise be entitled to overtime compensation,” and “each employee will be credited as if he or she had worked his or her normal work schedule for that shift.” 29 C.F.R. § 553.31(a). The plaintiffs read this regulation as requiring the City to pay overtime wages to the scheduled employee. The City contends that the regulation is void because a statute governing overtime, 29 U.S.C. § 207(a)(1), requires that a person actually work more than the statutory maximum number of hours to receive overtime pay.
When reviewing an agency’s construction of a statute, we look first to whether the statute’s language and legislative history clearly demonstrate what Congress intended. North Dakota ex rel. Olson v. Centers for Medicare & Medicaid Sens., 403 F.3d 537, 539 (8th Cir.2005). When they do, that intent controls and a court will not defer to any regulation that interprets the statute in a contrary manner. Id; see also Chevron U.S.A., Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 843, 845, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984). But when Congress’s intent is unclear and the statute contains an explicit or implicit gap, we will defer to the agency’s regulation so long as it is not “arbitrary, capricious, or manifestly contrary to the statute.” Id. at 844, 104 S.Ct. 2778; Friends of the Boundary Waters Wilderness v. Bosworth, 437 F.3d 815, 821-22 (8th Cir.2006).
In support of its plain-language argument, the City cites to language in the FLSA that says “no employer shall employ [673]*673any of his employees who in any workweek is engaged in commerce or in the production of goods for commerce, or is employed in an enterprise engaged in commerce or in the production of goods for commerce, for. a workweek longer than forty hours unless such employee receives [overtime wages].” 29 U.S.C. § 207(a)(1) (emphasis added). This language, the City says, means that the employee must be engaged (i.e., actively working) to receive overtime wages. But a more careful parsing of the section reveals that the statute uses the phrase “engaged in commerce” as a kind of applicational threshold: The overtime provisions of § 207(a) apply if the employee is engaged in commerce or in the production of goods for commerce at any time during the work week. And even if the employee is not engaged in commerce or in the production of goods for commerce, § 207(a) applies if the “enterprise” for which he or she works is so engaged. Id. The word “engaged” therefore relates not to whether the employee was actively working, but whether the employee’s or enterprise’s work was of a certain kind.
We question, moreover, the applicability of § 207(a) to these current and former firefighters. Congress amended the FLSA in 1974 so that its provisions would apply to state and local employees. In the course of passing those amendments, the House and Senate agreed to a partial exemption to the overtime rules for firefighters and police officers. Section 207(k) of the FLSA reflects that compromise. Under that provision, state and local employers of firefighters are not bound to the seven-day work period in 207(a), but may instead extend the relevant work period to as long as 28 days. 29 U.S.C. § 207(k). In addition, an employer must pay overtime wages only if a firefighter’s total “tours of duty” exceed 212 hours in a 28-day work period; for shorter work periods, the ratio of 212 to 28 is used to compute how many hours must be in a firefighter’s total “tours of duty” before he or she is entitled to overtime pay. Id.; 29 C.F.R. § 553.230(c). We see no indication in § 207(k) that all of those hours must be worked by the employee him- or herself. We therefore conclude that the FLSA’s plain language does not reveal a Congressional intent to deny an employee overtime wages when another worker voluntarily substitutes for him or her with the employer’s permission.
Examining the legislative history surrounding § 207(p)(3) helps clarify matters. This provision was part of the 1985 FLSA amendments, see Fair Labor Standards Amendments of 1985, PL 99-150 § 3(a), 99 Stat. 787 (November 13, 1985), and both the House and Senate Reports regarding those amendments note that employees engaged in fire-protection or law-enforcement activities traditionally traded shifts with one another without the substitution affecting the computation of overtime for either employee. H.R.Rep. No. 99-331, at 25 (1985); S.Rep. No. 99-159, at 13 (1985), U.S.Code Cong. & Admin.News 1985, 651, 661. The concern arose that without § 207(p)(3), certain FLSA regulations could require the state or local government to pay overtime to the substitute employee. Consider our earlier example, assuming that § 207(p)(3) did not exist. Employee B still works eight hours on behalf of employee A: If the FLSA requires the employer to pay employee B overtime for all the hours that he or she works above the statutory maximum, the employer would have to pay employee B twelve hours of overtime rather than four. Such a rule would leave the employer unable to control its overtime expenditures, since the employees’ voluntary substitutions could cause some employees to accrue massive amounts of overtime. The only way that the employer could cabin these costs would [674]*674be to forbid voluntary substitutions altogether, which would deprive both employers and employees of a useful and flexible tool.
Addressing this concern, both the House and Senate Reports explain that under the new subsection (§ 207(p)(3)), “[i]f two employees trade hours ..., each employee will be credited as if he or she had worked his or her normal work schedule.” H.R.Rep. No. 99-331, at 25 (1985); S.Rep. No. 99-150, at 13 (1985), U.S.Code Cong. & AdmimNews 1985, 651, 661. This is a clear indication that the purpose of § 207(p)(3) was to fashion a way to allow voluntary substitutions without having overtime costs spiral out of control. By having the employer credit each employee for the shift to which he or she was scheduled, the subsection limits the amount that an employer will have to pay in overtime wages to no more than what it would have paid absent the voluntary shift substitutions. The Department of Labor used exactly the same language when it promulgated § 553.31(a). The regulation as written is therefore fully consistent with the clearly expressed intent of Congress.
Even though the regulation as written is plainly consistent with Congress’s intent, we are still left with a question: What precisely does the regulation mean when it says that each employee will be “credited”? The City contends that the word “credited” requires it to give the scheduled employee only normal wages for the shift along with any attendant benefits that he or she would have accrued. The plaintiffs, on the other hand, argue that it means that the employer must treat the scheduled employee in all respects as if he or she had worked the shift, including paying him or her overtime wages if otherwise warranted. These arguments demonstrate that the term is susceptible to two different interpretations; in other words, the regulation is ambiguous on the question. The Department of Labor has consistently interpreted the regulation to mean that “the employee scheduled to work receives credit (and compensation) as if he or she had worked.” Application of the Fair Labor Standards Act to Employees of State and Local Governments, 52 Fed.Reg.2012, 2018 (Jan. 16, 1987); see also Wage and Hour Opinion Letter, 2004 WL 3177870 (Nov. 23, 2004). The Department of Labor’s amicus brief in this case has reiterated that position. An agency’s interpretation of its own ambiguous regulation will stand so long as it is not “ ‘plainly erroneous or inconsistent with the regulation.’ ” Rain & Hail Ins. Serv. v. Federal Crop Ins. Corp., 426 F.3d 976, 979 (8th Cir.2005) (quoting Auer v. Robbins, 519 U.S. 452, 461, 117 S.Ct. 905, 137 L.Ed.2d 79 (1997)) (quotation marks and citations omitted). The agency’s interpretation in this case easily passes that test.
We do not see much merit in the City’s argument that the Department of Labor’s interpretation of § 553.31(a) creates an unreasonable burden on employers. All the City has to do is pay the scheduled employee as if he or she had worked the scheduled shift; it need not keep any additional records. And the City need not monitor all shift exchanges, because any voluntary substitutions that take place will not cause the employer’s actual overtime expenditures to vary from the expectations that it developed when it first scheduled the employees.
For the foregoing reasons, we revex-se both the grant of the defendant’s motion for summary judgment and the denial of the plaintiffs’ motion for partial summary judgment, and we remand the case for further proceedings not inconsistent with this opinion.