SOLUTION: A soakaway was dug by 5 men in 24 days.How many days would it take 15 men to dig,if they were to work at the same rate?

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Question 1162253: A soakaway was dug by 5 men in 24 days.How many days would it take 15 men to dig,if they were to work at the same rate?
Found 3 solutions by josgarithmetic, MathLover1, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The work rate for 1 man, r;
What WAS done, 1 job in 24 days, FIVE men having done it, 5r=1%2F24, this being the work rate of the five men.



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How many days would it take 15 men to dig,if they were to work at the same rate?
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Which same rate? If you mean, each man still works at the same rate r, then you have unknown days, d;

15r%2Ad=1
Notice that this is three times the rate of the other group of men.

3%2A%285r%29d=1
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3%281%2F24%29d=1-----------now solve for d.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

shortest way:
5 men 24 days
15 men 3 times as many men means it takes+1%2F3 as long->24%2F3=+8 days
or this way:
5 men work at the rate of 1%2F24 hole per day
1+man works at the rate of 1%2F%285%2A24%29=1%2F120 hole per day
15 men works at the rate of 15%2F120 hole per day
So, our equation to solve is:
%2815%2F120%29x=1 (1 hole, that is)
15x=120
x=120%2F15
x=8 days


Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
Three times more workforce implies three times less work-time.


ANSWER.  8 days.