SOLUTION: If 6 men take 3 days to dig 8 ditches, then how long would it take 4 men to dig 10 ditches? Assume that all the ditches are the same size and take equally long to dig, and that all
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-> SOLUTION: If 6 men take 3 days to dig 8 ditches, then how long would it take 4 men to dig 10 ditches? Assume that all the ditches are the same size and take equally long to dig, and that all
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Question 963566: If 6 men take 3 days to dig 8 ditches, then how long would it take 4 men to dig 10 ditches? Assume that all the ditches are the same size and take equally long to dig, and that all the men work at the same steady rate.
I am having some problems finishing this problem. The rate of 1 ditch by the 6 men is 3/8 of a day. 1 person would take 2 1/4 days for 1 ditch. This is as far as I get before getting lost any help would be appreciated. Thank you Found 2 solutions by Fombitz, Edwin McCravy:Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website! Look at the number of man-days to build 1 ditch, to get the 1 man rate.
So then, 4 men to dig 10 ditches would be,
If you assume they work 8 hours in one day,
You can put this solution on YOUR website! If 6 men take 3 days to dig 8 ditches, then how long would it take 4 men to dig
10 ditches? Assume that all the ditches are the same size and take equally long
to dig, and that all the men work at the same steady rate.
You got this far:
The rate of 1 ditch by the 6 men is 3/8 of A DITCH PER day.
1 person would take 2 1/4 days for 1 ditch.
So 4 men would take 1/4 of 2 1/4 days for 1 ditch.
That's (1/4)(2 1/4) = (1/4)(9/4) = (9/16) of a day for 1 ditch.
Therefore it would take them 10 times as long for 10 ditches.
(9/16)(10) = 90/16 = 45/8 = 5 5/8 days.
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Another way to do it is:
The LCM of 6 men and 4 men is 12 men
Since 6 men take 3 days to dig 8 ditches, then
12 men take 1 1/2 or 3/2 days to dig 8 ditches.
So 4 men would take 3 times as long or 9/2 days to dig 8 ditches
So 4 men would take 1/8th of 9/2 days, or 9/16ths of a day to dig 1 ditch.
So to dig 10 ditches, it would take them 10 times as long or
(9/16)(10) = 90/16 = 45/8 = 5 5/8 days.
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Another way to do it is:
The LCM of 8 ditches and 10 ditches is 40 ditches
Since 6 men take 3 days to dig 8 ditches, then
6 men take 15 days to dig 40 ditches.
So 6 men would take 15/4 days to dig 10 ditches
So 2 men would take 3 times as long or 45/4 days to dig 10 ditches.
So 4 men would take 1/2 of 45/4 days or 45/8 or 5 5/8 days to dig
10 ditches.
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The most straight-forward way is to use the worker-time-job formula, which is:
where
W1 = the number of workers in the first situation.
T1 = the number of time units (days in this case) in the first situation.
J1 = the number of jobs in the first situation.
W2 = the number of workers in the second situation.
T2 = the number of time units (days in this case) in the second situation.
J2 = the number of jobs in the second situation.
W1 = 6 W2 = 4
T1 = 3 T2 = the unknown quantity
J1 = 8 J2 = 10
reduces to and reduces to
Cross-multiply
8T2 = 45
Divide both sides by 8
T2 = 45/8 or 5 5/8.
Answer: 5 5/8 days.
Edwin
