# Math problem about hours worked and wages earned.In a regular week, there are 5 working days and for each day, the working hours are 8.A man gets \$ 2.40 per hour for regular work and \$ 3.20 per...

Math problem about hours worked and wages earned.

In a regular week, there are 5 working days and for each day, the working hours are 8.A man gets \$ 2.40 per hour for regular work and \$ 3.20 per hours for over-time. If he earns \$ 432 in 4 weeks, then how many hours does he work for?

hkj1385 | (Level 1) Assistant Educator

Posted on

Let the number of days worked be 'x' and the number of extra hours worked be 'y'

Thus, total hours worked = (8*x) + y...........(1)

Total amount gained = 2.4*(8*x) + (3.2*y) = 432............(2)

Now, there are 4 weeks and each week has 5 working days and each day with 8 regular working hours

Thus, total regular working hours in 4 weeks = 4*5*8 = 160 hours...........(3)

Using (3) in (2) we get

2.4*160 + (3.2*y) = 432

or, 384 + (3.2*y) = 432

or, 3.2*y = 48

or, y = 48/3.2 = 480/32 = 15

Thus, overtime hours = y = 15............(4)

Thus, total hours of working in 4 weeks = (3) + (4) = 160 + 15 = 175 hours.

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

He works 160 hours of regular work and 15 hours of overtime.

Here's how to arrive at this answer.

He works 8 hours a day, 5 days a week for 4 weeks.  This means you multiply 8*5 and get 40 hours per week and multiply that by 4 and get 160.

160 hours times \$2.40 per hour is \$384.

So then you subtract \$384 from \$432 and you get \$48.  That means he earned \$48 of overtime.

You divide \$48 by \$3.20 and you get 15.

So that's 160 hours of regular work and 15 of overtime.

tutorialguide | eNotes Newbie

Posted on

Suppose the man works over-time for x hours. Now, working hours in 4 weeks = (5 × 8 × 4) = 160. 160 × 2.40 + x × 3.20 = 432 ⇒ 3.20x = 432 – 384 = 48 ⇒ x = 15. Hence, total hours of work = (160 + 15) = 175.

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

It is not told what is the regular working hours in this problem.Hower , it is mentioned the working hours are 8. So we pressume that working beyond 8 hours is overtime and working 8 hours are regular and compulsory

Total working hours (pressumed to be regular) in 4 weeks at 8hours per day and 5 day a week = 8*5*4= 160  hours for which the earning at the rate of earning is \$2.4/h is 160*2.4 =\$384.

Since his total earned money of \$432 includes the above regular hour working earning of \$384, we conclude that \$432-\$384 = \$ 48 is his overtime earning for which he should work  a overtime of \$48/(\$3.2/h) = 15hours.

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

Given:

Working days per week = 5 days

Regular working hours per day = 40 hours

Normal wage rate = \$2.40 per hour

Over-time wage rate = \$3.2 per hour

Total weeks worked = 4 weeks

Total earning for 4 weeks = \$432

The total normal working hours for 4 week:

= 4 x (Working hours per week) = 4 x 40 = 160 hours

Wages for normal work for 160 hours:

= 160 x (normal wages per hour) = 160 x 2.4 = 384 \$

Wages for over-time:

= (Total earnings) - (Wages for normal work) = 432 - 384 = 48 \$

Over-time hours worked:

(Wages for over-time)/(Over-time wage rate)

= 48/3.2 = 15 hours.

Total hours worked:

= (Normal working hours for 4 week) - (Over-time hours worked)

= 160 + 15 = 175 hours