# 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?

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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.

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.

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.

For more information on math problems, log on to http://examville.com You can take online practice tests, browse live review classes, and share and download study guides at Examville.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.

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

Answer:

He works for 175 hours.