GIBSON, Chief Judge.
Plaintiff, Loraine Mumbower,1 appeals from a judgment for defendants following the non-jury trial of her complaint alleging violations of the maximum hour and overtime pay provisions of the Fair Labor Standards Act of 1938 (FLSA), 29 U.S.C. § 201 et seq. (1970), as amended, 29 U.S.C. § 201 et seq. (Supp. Ill, 1973). She seeks to recover unpaid overtime compensation and attorney’s fees for approximately 1271 hours of work as the sole switchboard operator of defendants’ K-M Telephone Answering Service, a partnership,2 from August 1, 1970, until August 10, 1973.
The District Court entered judgment for defendants on May 9, 1975, holding that as plaintiff was hired on a weekly not an hourly basis, even assuming she worked all hours alleged, her pay exceeded the current minimum wage for overtime. Thus, she was not entitled to additional compensation.
On appeal, plaintiff contends that (1) the court erred in calculating her hourly time and a half compensation on the basis of the minimum wage rather than her “regular rate,” and (2) erred in calculating her actual working hours by failing to include working lunch periods and time before and after the switchboard was. open during which she performed additional duties. We reverse the District Court’s judgment and remand for an award of unpaid overtime compensation on the basis of recalculated hours.
Prior to July 26, 1968, plaintiff worked with three other women as a part-time switchboard operator for the answering service, then partly owned by her ex-husband, defendant Callicott. On that date Callicott and others purchased the business from the joint owners and managed it until defendants Schaefer and Barks assumed command in July, 1973. [1186]*1186At the time of the purchase by Callicott, plaintiff agreed to operate the switchboard by herself for $80 per week, maintaining the same hours as before, 8:00 a. m. to 6:00 p. m., six days per week, with one hour for lunch. Up to the time of her discharge in August, 1973, her hours gradually decreased and pay increased.3
Plaintiff had her own key to the premises and served as her own supervisor. The fifty-line, single-operator switchboard was located in a six foot square, windowless room. Callicott occupied a nearby office. Plaintiff testified that Callicott determined the hours the switchboard was to be open. However, no employment records were maintained. She testified that she arrived early on a regular basis and usually received a call from Callicott at 7:30 a. m. with instructions for the day. He requested her to perform duties such as admitting the janitor, opening the mail, posting checks, maintaining a record of accounts in Callicott’s office, obtaining the appointment book of a customer, Dr. Walter, from his nearby office to take the day’s appointments, reviewing customers’ daily itineraries, and meeting with customers who picked up their packages and messages. These duties she performed regularly between 7:30 a. m. and 8:00 a. m. with Callicott’s knowledge and “tacit” approval before the switchboard opened. Callicott specifically approved the special routine for Dr. Walter.
Plaintiff also testified that she was instructed by Callicott to remain on duty after the switchboard officially closed to transmit daily messages to customers calling in. Her hours thus extended fifteen to thirty minutes beyond the official closing time. During this time she would also empty trash, lock the office and turn off lights. Callicott occasionally called to remind her of these and other duties. She further testified that she had complained of her inability to take lunch periods because no one was available to replace her. Over the years she worked through occasional illnesses and eventually in July, 1972, was hospitalized for fatigue for several weeks. During her hospital stay she was replaced by another operator whom she had trained in advance. After her discharge in August, 1973, she was replaced by two part-time operators, each working half days.
The District Court relied primarily upon plaintiff’s own recollections to determine the number of hours she worked on the switchboard from August, 1970, until August, 1973. To do so was proper, as defendants maintained none of the employment records required by the FLSA, 29 U.S.C. § 211(c); 29 C.F.R. § 516.1 et seq. (1974), and will not be permitted to benefit from their failure to do so. See Brennan v. Maxey’s Yamaha, Inc., 513 F.2d 179, 183 (8th Cir. 1975). Relying upon plaintiff’s recollections, the court found that she operated the switchboard for periods of 54, 48, 44 and 40 hours per week respectively at various times during the period embraced by the complaint.4 However, these findings did not include the working lunch periods and times before and after the scheduled switchboard hours during which plaintiff claims she performed additional duties. Nonetheless, assuming she worked all the hours claimed, the court held she was not entitled to additional overtime compensation [1187]*1187for the reason that her overall pay was in excess of the current minimum wage of $1.60 per hour. Calculating the employee’s pay on the basis of the minimum wage, however, rather than her “regular rate,” was erroneous.
Section 7(a) of the FLSA requires an employee to be paid overtime compensation for hours worked in excess of forty per week “at a rate not less than one and one-half times the regular rate at which he is employed.” 29 U.S.C. § 207(a)(1). (Emphasis added.) This provision has been uniformly interpreted to require the fifty percent overtime premium to be added to the actual wage paid, not to the statutory minimum wage for hours up to forty, with the “intended effect” of requiring extra pay for overtime even for employees whose hourly wages exceed the statutory minimum. Overnight Motor Co. v. Missel, 316 U.S. 572, 577, 62 S.Ct. 1216, 86 L.Ed. 1682 (1942); accord, Warren-Bradshaw Drilling Co. v. Hall, 317 U.S. 88, 93, 63 S.Ct. 125, 87 L.Ed. 83 (1942); Brennan v. Lauderdale Yacht Basin, Inc., 493 F.2d 188, 189-90 (5th Cir. 1974). This principle applies to employees hired on a weekly as well as an hourly basis.
If the parties wish to modify the statutory rule by contracting for a “regular rate” of pay greater than the minimum wage, they may do so provided the employee is paid time and one-half the regular rate for hours over forty per week. See, e. g., Walling v. A. H. Belo Corp., 316 U.S. 624, 631-32, 62 S.Ct. 1223, 86 L.Ed. 1716 (1942).
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GIBSON, Chief Judge.
Plaintiff, Loraine Mumbower,1 appeals from a judgment for defendants following the non-jury trial of her complaint alleging violations of the maximum hour and overtime pay provisions of the Fair Labor Standards Act of 1938 (FLSA), 29 U.S.C. § 201 et seq. (1970), as amended, 29 U.S.C. § 201 et seq. (Supp. Ill, 1973). She seeks to recover unpaid overtime compensation and attorney’s fees for approximately 1271 hours of work as the sole switchboard operator of defendants’ K-M Telephone Answering Service, a partnership,2 from August 1, 1970, until August 10, 1973.
The District Court entered judgment for defendants on May 9, 1975, holding that as plaintiff was hired on a weekly not an hourly basis, even assuming she worked all hours alleged, her pay exceeded the current minimum wage for overtime. Thus, she was not entitled to additional compensation.
On appeal, plaintiff contends that (1) the court erred in calculating her hourly time and a half compensation on the basis of the minimum wage rather than her “regular rate,” and (2) erred in calculating her actual working hours by failing to include working lunch periods and time before and after the switchboard was. open during which she performed additional duties. We reverse the District Court’s judgment and remand for an award of unpaid overtime compensation on the basis of recalculated hours.
Prior to July 26, 1968, plaintiff worked with three other women as a part-time switchboard operator for the answering service, then partly owned by her ex-husband, defendant Callicott. On that date Callicott and others purchased the business from the joint owners and managed it until defendants Schaefer and Barks assumed command in July, 1973. [1186]*1186At the time of the purchase by Callicott, plaintiff agreed to operate the switchboard by herself for $80 per week, maintaining the same hours as before, 8:00 a. m. to 6:00 p. m., six days per week, with one hour for lunch. Up to the time of her discharge in August, 1973, her hours gradually decreased and pay increased.3
Plaintiff had her own key to the premises and served as her own supervisor. The fifty-line, single-operator switchboard was located in a six foot square, windowless room. Callicott occupied a nearby office. Plaintiff testified that Callicott determined the hours the switchboard was to be open. However, no employment records were maintained. She testified that she arrived early on a regular basis and usually received a call from Callicott at 7:30 a. m. with instructions for the day. He requested her to perform duties such as admitting the janitor, opening the mail, posting checks, maintaining a record of accounts in Callicott’s office, obtaining the appointment book of a customer, Dr. Walter, from his nearby office to take the day’s appointments, reviewing customers’ daily itineraries, and meeting with customers who picked up their packages and messages. These duties she performed regularly between 7:30 a. m. and 8:00 a. m. with Callicott’s knowledge and “tacit” approval before the switchboard opened. Callicott specifically approved the special routine for Dr. Walter.
Plaintiff also testified that she was instructed by Callicott to remain on duty after the switchboard officially closed to transmit daily messages to customers calling in. Her hours thus extended fifteen to thirty minutes beyond the official closing time. During this time she would also empty trash, lock the office and turn off lights. Callicott occasionally called to remind her of these and other duties. She further testified that she had complained of her inability to take lunch periods because no one was available to replace her. Over the years she worked through occasional illnesses and eventually in July, 1972, was hospitalized for fatigue for several weeks. During her hospital stay she was replaced by another operator whom she had trained in advance. After her discharge in August, 1973, she was replaced by two part-time operators, each working half days.
The District Court relied primarily upon plaintiff’s own recollections to determine the number of hours she worked on the switchboard from August, 1970, until August, 1973. To do so was proper, as defendants maintained none of the employment records required by the FLSA, 29 U.S.C. § 211(c); 29 C.F.R. § 516.1 et seq. (1974), and will not be permitted to benefit from their failure to do so. See Brennan v. Maxey’s Yamaha, Inc., 513 F.2d 179, 183 (8th Cir. 1975). Relying upon plaintiff’s recollections, the court found that she operated the switchboard for periods of 54, 48, 44 and 40 hours per week respectively at various times during the period embraced by the complaint.4 However, these findings did not include the working lunch periods and times before and after the scheduled switchboard hours during which plaintiff claims she performed additional duties. Nonetheless, assuming she worked all the hours claimed, the court held she was not entitled to additional overtime compensation [1187]*1187for the reason that her overall pay was in excess of the current minimum wage of $1.60 per hour. Calculating the employee’s pay on the basis of the minimum wage, however, rather than her “regular rate,” was erroneous.
Section 7(a) of the FLSA requires an employee to be paid overtime compensation for hours worked in excess of forty per week “at a rate not less than one and one-half times the regular rate at which he is employed.” 29 U.S.C. § 207(a)(1). (Emphasis added.) This provision has been uniformly interpreted to require the fifty percent overtime premium to be added to the actual wage paid, not to the statutory minimum wage for hours up to forty, with the “intended effect” of requiring extra pay for overtime even for employees whose hourly wages exceed the statutory minimum. Overnight Motor Co. v. Missel, 316 U.S. 572, 577, 62 S.Ct. 1216, 86 L.Ed. 1682 (1942); accord, Warren-Bradshaw Drilling Co. v. Hall, 317 U.S. 88, 93, 63 S.Ct. 125, 87 L.Ed. 83 (1942); Brennan v. Lauderdale Yacht Basin, Inc., 493 F.2d 188, 189-90 (5th Cir. 1974). This principle applies to employees hired on a weekly as well as an hourly basis.
If the parties wish to modify the statutory rule by contracting for a “regular rate” of pay greater than the minimum wage, they may do so provided the employee is paid time and one-half the regular rate for hours over forty per week. See, e. g., Walling v. A. H. Belo Corp., 316 U.S. 624, 631-32, 62 S.Ct. 1223, 86 L.Ed. 1716 (1942). However, such a modification must be clearly agreed upon. Brennan v. Valley Towing Co., 515 F.2d 100, 105-06 (9th Cir. 1975). For employees paid weekly, absent explicit proof of a mutual agreement for a rate of pay capable of delineation in hourly terms, the court must infer that the “regular rate” is substantially that calculated by dividing the total weekly compensation by the number of hours scheduled in the workweek. Overnight Motor Co. v. Missel, supra at 580 n. 16; Brennan v. Valley Towing Co., supra at 106; see 29 C.F.R. § 778.325 (1974). In the instant case no explict agreement was made, stipulating a weekly wage inclusive of regular and overtime compensation for a workweek in excess of forty hours, from which the appropriate “regular” hourly rate can be derived by formula. 149 Madison Avenue Corp. v. Asselta, 331 U.S. 199, 204, 67 S.Ct. 1178, 91 L.Ed. 1432 (1947). Consequently, on remand plaintiff’s actual “regular rate” of pay must be recalculated by dividing her weekly salary by the number of scheduled hours worked and her overtime compensation reassessed at time and a half her regular rate for the period embraced by the complaint.5
On remand it will also be necessary to reassess the number of. hours actually worked by plaintiff for the reason that the District Court’s computation was apparently induced by an erroneous view of the law defining hours worked. The court held that the plaintiff was not entitled to be paid for her lunch hours spent at the switchboard, nor for the time she performed duties before and after the scheduled switchboard hours, because such work was not part of “her arrangement as to when she would keep the board open.” However, liability under the Act depends not upon formal or agreed arrangements between employer and employee limiting work hours but upon the number of hours the employee [1188]*1188is actually permitted to work for the employer’s benefit. Handler v. Thrasher, 191 F.2d 120, 123 (10th Cir. 1951); Republican Publishing Co. v. American Newspaper Guild, 172 F.2d 943, 945 (1st Cir. 1949); see 29 U.S.C. § 203(g) (“ ‘Employ’ includes to suffer or permit to work.”).
The term “work” is not defined in the FLSA, but it is settled that duties performed by an employee before and after scheduled hours, even if not requested, must be compensated if the employer “knows or has reason to believe” the employee is continuing to work, 29 C.F.R. § 785.11 (1974), and the duties are an “integral and indispensable part” of the employee’s principal work activity. Steiner v. Mitchell, 350 U.S. 247, 256, 76 S.Ct. 330, 100 L.Ed. 267 (1956); 29 C.F.R. §§ 785.24 and 785.25 (1974). Plaintiff contends that she regularly performed morning duties before officially opening the board and afternoon duties after scheduled closing, and that such extra work was knowingly permitted by the managing partner. If so, she is entitled to be compensated therefor at her regular rate. The employer who wishes no such work to be done has a duty to see it is not performed. He cannot accept the benefits without including the extra hours in the employee’s weekly total for purposes of overtime compensation. If the employer has the power and desire to prevent such work, he must make every effort to do so. 29 C.F.R. § 785.13 (1974).
A similar rule applies to meal periods during which an employee is not completely relieved of duty. 29 C.F.R. § 785.19 (1974). Plaintiff testified without contradiction that she was not relieved during lunch periods. Defendants Barks and Schaefer conceded that fact during oral argument in this court. The record also indicates that two of the defendants were informed that no replacement operator was available and that plaintiff wished to be relieved, but none was provided. The nature of the answering service business requires noon hour coverage and plaintiff apparently continued to operate the switchboard in a conscientious effort to avoid losing customers, not because she was ordered to do so. Such extra work for the employer’s benefit and with his tacit approval must be included in determining whether overtime compensation is statutorily required.
A contrary holding would be detrimental to the Act’s legislative policy of spreading work to more employees by requiring employers to pay each individual a premium for excessive hours. Overnight Motor Co. v. Missel, 316 U.S. 572, 577-78, 62 S.Ct. 1216, 86 L.Ed. 1682 (1942); Brennan v. Elmer’s Disposal Service, Inc., 510 F.2d 84, 87 (9th Cir. 1975). Defendants’ contention that plaintiff agreed to the conditions of her scheduled workweek is no defense. There was no explicit agreement on rate of pay for regular hours or overtime pay for extra hours over 40. No records were kept of the hours actually worked or the regular rate applicable to the hours. The employer’s obligation to pay premium overtime compensation, whatever the regular rate of pay, is statutory and cannot be waived or substituted by an agreement to work for less. Mitchell v. Turner, 286 F.2d 104, 106 (5th Cir. 1960); Mitchell v. Greinetz, 235 F.2d 621, 625 (10th Cir. 1956).
The judgment of the District Court is reversed and the case remanded for an award of unpaid overtime compensation on the basis of hours recalculated in a manner consistent with this opinion.