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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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.

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.

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.

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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