SOLUTION: 30men can paint an estate in 48hours. after working for 20hours 6men left.how much longer did they take to complete the work.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 30men can paint an estate in 48hours. after working for 20hours 6men left.how much longer did they take to complete the work.      Log On


   

Question 1144739: 30men can paint an estate in 48hours. after working for 20hours 6men left.how much longer did they take to complete the work.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
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If the group is 30 men, and after 20 hours, 6 left, the 24 men remain to finish the job.

r, one man rate
x, time to finish after some men left

system%2830r%2A48=1%2C30%2Ar%2A20%2B24%2Ar%2Ax=1%29

r=1%2F%2830%2A48%29
-
30%281%2F%2830%2A48%29%2920%2B24%281%2F%2830%2A48%29%29x=1
20%2F48%2Bx%2F60=1
.
.
highlight%28x=35%29

Answer by ikleyn(52905) About Me  (Show Source):
You can put this solution on YOUR website!
.
(1)  Since 30 men can do the job in 48 hours, their rate of work is  1%2F%2830%2A48%29 part of job per 1 man per hour.


(2)  After working for 20 hours, 30 men completed  20%2F48 = 5%2F12 of the job;

     hence,  1 - 5%2F12 = 7%2F12 remained to complete.


(3)  How many time will it take for 24 remained men to complete  7%2F12 of the job ?

     Divide the remaining job by 24%2F%2830%2A48%29 = 1%2F60.  You will get

          remaining time = %28%287%2F12%29%29%2F%28%281%2F60%29%29 = %287%2A60%29%2F12 = 35.


ANSWER.  35 hours after 6 men left out.