SOLUTION: 8 dug 3/8 of tunnel in 10 days. If they need to finish the remaining 5/8 of the tunnel in 7/3 days, how many more workers must they hire?

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Question 678128: 8 dug 3/8 of tunnel in 10 days. If they need to finish the remaining 5/8 of the tunnel in 7/3 days, how many more workers must they hire?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
8 dug 3/8 of tunnel in 10 days.
If they need to finish the remaining 5/8 of the tunnel in 7/3 days, how many more workers must they hire?
:
80 man-days to do 3/8 of the tunnel
:
let x = no. of man-days to do 5/8 of the tunnel
:
80%2Fx = %283%2F8%29%2F%285%2F8%29
Cross multiply
3%2F8x = 5%2F8*80
3%2F8x = 50
x = 8%2F3*50
x = 133.33 man-days to do 5/8 of the tunnel
:
let w = additional workers needed to finish in 7/3 days
7%2F3(w+10) = 133.33
Multiply both sides by 3
7(w + 10) = 3(133.33)
7w + 70 = 400
7w = 400 - 70
7w = 330
w = 330/7
w ~ 47 additional men required
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Check this:
7%2F3*57 = 133.33 man-days, the amt needed to do 5/8 of the job