With certain exceptions not here relevant, Section 7 of the Fair Labor Standards Act [ 63 Stat. 912 (1949) as amended, 29 U.S.C. § 207 (Supp. IV 1959-62)] requires employers to pay employees “time and a half” for all hours in excess of 40 worked during a single work week; and this provision “obviously and necessarily includes one compensated by a unit of time, by the piece or by any other measurement.” United States v. Rosenwasser, 323 U.S. 360, 363 , 65 S.Ct. 295, 296-297 , 89 L.Ed. 301 (1945).

Contending that the Dix Box Co. and Benjamin Dix, its sole shareholder (Dix) had failed to comply with this provision of the Act, the Secretary of Labor commenced this suit on behalf of several Dix employees to recover the extra compensation they claimed for overtime.

The employees who are concerned in this appeal were hired to make and repair produce boxes and perform various tasks. They were paid at a piece rate for box work and by the hour for the remainder of their services.

At the trial the principal issue was how many hours in all these employees had worked during each of the weeks under consideration.

As part of his proof the Secretary offered and the court admitted into evidence the records Dix had kept of their time and earnings. These consisted of tabulations made daily of the number of hours each employee had devoted to hourly work and the amount of his combined earnings for both that and piece work. The accuracy of the figures is unquestioned. From these records it appeared that several of the employees had accumulated 40 or more hours at hourly work alone during periods under consideration; it also appeared that during these same periods some of the employees had additional earnings from piece work, thus clearly indicating still more time for which they were entitled to extra compensation. Dix, however, had not recorded this time and to that extent at least had failed to comply with the requirements of Section 11(c) of the Act [ 52 Stat. 1066 (1938), as amended, 29 U.S.C. § 211 (c) (1958)] and pertinent regulations promulgated thereunder by the Secretary of Labor (29 C.F.R. 516) which made it the duty of employers to keep an accurate and complete account of the total number of hours worked by their employees. And apparently Dix employees had not made any memoranda of their time either.

In an effort to supply the missing information, the Secretary asked each em ployee to give an estimate of his average hourly earnings from piece work. However, the trial court sustained an objection to these questions and rejected the Secretary’s ensuing offers of proof on the ground that such testimony, relating to matters about three years before the trial, “would be speculation as a matter of law.”

The Secretary also sought to introduce several records, covering periods immediately following those under consideration, which Dix itself had made and which contained tabulations showing the hourly productivity and piece work earnings of some of these employees. This documentary evidence was offered in connection with and to supplement the employees’ testimony regarding their estimated piece work earnings and to corroborate such testimony. But the court ruled that this latter proof was irrelevant and inadmissible.

The Secretary then rested, Dix submitted no proof and the court, sitting as finder of fact, granted judgment for the Secretary but limited to the amounts reflecting only those overtime hours which Dix’s records themselves showed. On appeal, the Secretary urges that the trial court erred in excluding this evidence.

In a suit of this kind an employee should not be denied recovery merely because he cannot prove the precise extent of uncompensated work. The court in Anderson v. Mt. Clemens Pottery Co., 328 U.S. 680 , 66 S.Ct. 1187 , 90 L.Ed. 1515 (1946) made it clear that where an employer’s records are inaccurate or inadequate “an employee has carried out his burden if he proves that he has in fact performed work for which he was improperly compensated and if he produces sufficient evidence to show the amount and extent of that work as a matter of just and reasonable inference.” Id., 328 U.S. at 687 , 66 S.Ct. at 1192 , 90 L.Ed. 1515 .

We are convinced that the proffered testimony meets that test. A sufficient foundation was laid for its admission and, although the result obtained from its use would obviously not reflect the exact amount of time the witness in fact had worked, we think that it would provide a basis for a determination of that fact with reasonable accuracy.

We likewise must disagree with the trial court’s conclusion that the documentary evidence consisting of records Dix kept of these employees’ earnings immediately following the periods covered by the complaint was irrelevant. It appears that the Secretary was prepared to show that the piece work the employees performed during all periods was essentially the same, and thus it would not be unreasonable to infer that the rates of their hourly piece work earnings were likewise about the same. 3 Moreover, had the court admitted the em ployees’ testimony regarding their hourly earnings (as it should have) then these records would tend to corroborate that testimony and to that extent were relevant and should have been admitted. See 20 Am.Jur. Evidence § 248 (1939). Pertinent is the admonition of the Supreme Court that employees must not be held to a standard of proof which would have the practical effect of impairing many of the benefits of the Act: “The remedial nature of this statute and the great public policy which it embodies * * * militate against making that burden [of proof] an impossible hurdle for the employee. Due regard must be given to the fact that it is the employer who has the duty under § 11(c) of the Act to keep proper records of wages, hours, and other conditions and practices of employment and who is in position to know and to produce the most probative facts concerning the nature and amount of work performed.” Anderson v. Mt. Clemens Pottery Co., supra, 328 U.S. at p. 687 , 66 S.Ct. at p. 1192 , 90 L.Ed. 1515 .

The judgment is vacated and the action is remanded to the District Court with directions to grant a new trial.

. “§ 207. Maximum hours. “(a) (1) Except as otherwise provided in this section, no employer shall employ any of his employees who in any workweek is engaged in commerce or in the production of goods for commerce for a woi'kweek longer than forty hours, unless such employee receives compensation for his employment in excess of the hours above specified at a rate not less than one and one-half times the regular rate at which he is employed * * . The tenor of the employees’ proof would have been that their respective hourly earnings from piece work differed from their fixed hourly pay. This would pose the problem of how much of either kind of work was performed during the 40 hours for which no overtime was paid. Recognizing this difficulty the Wage-Hour Investigator had computed the amount claimed due on the basis of a formula under which he determined the weighted average hourly earning rate for both types of work combined: He first divided the wages actually paid during the week by the hours actually worked and then multiplied the overtime hours by one-half the average hourly rate. To illustrate: Robert Garmon would have testified he averaged about $3.00 per hour at piece work. Dix’s records showed that in the .week ending April 11, 1959 Garmon was paid $122.00 for hourly work at $2.00 per hour and, in addition, $17.19 for piece work, making a total of $139.19. He worked 61 hours at hourly work and (accepting his testimony of $3.00 an hour from piece work) 5% hours doing piece work, for a total of 66% hours. This latter figure divided into his total weekly pay of $139.19 shows his average hourly pay was $2.09. One-half of $2.09 multiplied by 26% (Garmon’s overtime hours) is $27.69, his unpaid overtime. This formula accords with the “rule” approved in Bay Ridge Operating Co. v. Aaron, 334 U.S. 446, 459-460 , 68 S.Ct. 1186 , 92 L.Ed. 1502 (1948).