Question

12 laborers could finish a roadwork in 17 days. After 11 days, 5 laborers quit and are not replaced until 4 days.
(a) How many more laborers should be added to complete the job on time?
(b) How much was paid for labor if during the last portion of the job, the sum of 55 was paid on wages?

Answer 1

How to solve this using one unknown?

Answer 2

since this is a work problem, you first need to find the rate of each laborer per day..
Rate will be:
\[R = \frac{ 1 }{ nt }\]
where R is the rate
n is the number of laborers
t is the time
now solve for the rate given the first condition that 12 workers could finish the work in 17 days

Answer 3

what did you get?

Answer 4

So, R = 1/(12)(17)

Answer 5

which is 1/204

Answer 6

What should I do next?

Answer 7

yep

Answer 8

now we'll try to make an equation out of the next condition
since it is given that 12 men were working for 11 days, 12-5 men for the next 4 days, and they need to finish the job in the next 17-11-4 days, then we'll have it as
R(12men)(11days) + R(7men)(4days) + R(n)(2days) = 1
now you substitute the rate of work per worker per day

Answer 9

1 there represents one work done

Answer 10

\[\frac{40}{ 50 } +\frac{1}{ 102 }n = 1 \]

Answer 11

@shinalcantara What next?

Answer 12

try to recheck 40/50.. i think it's 40/51

Answer 13

oh sorry, it is 40/51.

n = 22

Is this correct?

Answer 14

yep but since n there is the total number of workers necessary to finish the job for the last two days and there are already 7 men working at that time, therefor the addition number of workers needed will be n-7

Answer 15

*additional

Answer 16

n-7 = 22-7 = 15

Answer 17

yep

Answer 18

Ok. Thanks. What about the next question?

Answer 19

Since you already know the number of workers for the last portion of the job, n=22,
and the time is t=2days, and you're given the wage to be 55 so,
payment for 1worker for 1 day would be Payment=55/(nt)

Answer 20

The answer of that will be the rate of Payment

Answer 21

Payment = 1.25

Answer 22

To find the total payment you'll have
let P be the rate of payment and Pt be the total labor cost for the entire work.
so you'll have
Pt = P(12)(11) + P(7)(4) + P(22)(2)

Answer 23

Ok, got it! Thank you so much!

Answer 24

ok. yw:)