Question

Given that 224 hours of work need to be done to complete a project. (1) How long will it take 4 men, each working an 8-hour day to complete the project? (II) If each of them is paid 57-50 per hour, how much will it cost to employ them altogether? (iii) How many hours of overtime must they put in per day if the project is to be completed in 4 days? (iv) Given that the overtime rate of payment is l times as much as the regular hourly rate, find the cost of the project now. ​

Answer 1

Explanation:

(i) To complete the project, 4 men will need to work a total of 224 hours. Each man works for 8 hours per day. Therefore, the number of days it will take to complete the project is:

Number of days = 224 total hours / (4 men x 8 hours/day) = 7 days

So it will take 4 men, each working 8 hours per day, 7 days to complete the project.

(ii) Each man is paid $57.50 per hour, and they will work for a total of 7 x 8 = 56 hours altogether. Therefore, the total cost of employing them all is:

Total cost = 4 men x $57.50/hour x 56 hours = $12,320

(iii) If the project is to be completed in 4 days, each man will need to work for a total of:

224 total hours / (4 men x 4 days) = 14 hours per day

Since each man already works for 8 hours per day, they will need to put in an additional 6 hours of overtime per day to complete the project in 4 days.

(iv) The regular hourly rate is $57.50 per hour, and the overtime rate is 1.5 times the regular hourly rate (150% of the regular hourly rate). Therefore, the overtime rate is:

Overtime rate = $57.50 x 1.5 = $86.25/hour

To find the total cost of the project, we need to add the cost of the regular hours and the cost of the overtime hours. The cost of the regular hours is:

Regular hours cost = 224 regular hours x $57.50/hour = $12,880

The cost of the overtime hours is:

Overtime cost = (4 men x 6 overtime hours/man/day x 4 days) x $86.25/hour

= 96 x $86.25

Therefore, the total cost of the project is:

Total cost = Regular hours cost + Overtime cost

= $12,880 + $8,280

= $21,160

where the overtime rate is 1.5 times the regular hourly rate.

Answer 2

If 4 men, each working an 8-hour day, have to complete 224 hours of work, then the number of days required to complete the work is:

Total number of hours of work / Number of hours of work done by 4 men in a day

= 224 / (4 x 8)

= 7

So, it will take 4 men, each working an 8-hour day, 7 days to complete the project.

II. Each of the 4 men will work for 7 days, and each man works 8 hours a day. So, the total number of hours worked by all the men is:

Total number of men x Total number of days x Number of hours worked by each man per day

= 4 x 7 x 8

= 224 hours

Therefore, the total cost of employing all 4 men is:

Total number of hours x Rate per hour

= 224 x $57.50

= $12,880

III. If the 4 men have to complete the project in 4 days, then the number of hours of work they have to do each day is:

Total number of hours of work / Total number of days to complete the project

= 224 / 4

= 56 hours

Each man works 8 hours a day, so the total number of hours of overtime they have to put in per day is:

Number of hours of work per day - Number of hours worked by each man per day

= 56 - 8

= 48 hours

Therefore, each man must put in 6 hours of overtime per day to complete the project in 4 days.

IV. If the overtime rate of payment is l times as much as the regular hourly rate, then the overtime rate of payment is:

l x $57.50

= $57.50l

Let the overtime rate of payment be $r per hour. Then:

r = $57.50l

The cost of the project is the sum of the cost of regular hours and the cost of overtime hours. The cost of regular hours is:

Number of regular hours x Regular hourly rate

= 4 x 8 x 7 x $57.50

= $16,240

The cost of overtime hours is:

Number of overtime hours x Overtime hourly rate

= 4 x 6 x 7 x $57.50l

= $12,180l

So, the total cost of the project is:

Total cost = Cost of regular hours + Cost of overtime hours

= $16,240 + $12,180l