SOLUTION: 10 men working for 5 hours a day for 6 days mow an area of 5 acres. If there are 8 men working 4 hours a day to mow 4 acres of land, how many days will it take.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 10 men working for 5 hours a day for 6 days mow an area of 5 acres. If there are 8 men working 4 hours a day to mow 4 acres of land, how many days will it take.      Log On


   

Question 1016652: 10 men working for 5 hours a day for 6 days mow an area of 5 acres. If there are 8 men working 4 hours a day to mow 4 acres of land, how many days will it take.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rate of working for the 1 man is:
[ acres ] / [ number of man*hrs ]
+5+%2F+%28+10%2A5%2A6+%29+=+1%2F60+ acres/( man*hrs )
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The rate of working does not change, so:
+1%2F60+=+4+%2F+%28+8%2A4d+%29+
Multiply both sides by +60%2A32d+
+32d+=+240+
+d+=+7.5+
It will take the 8 men 7.5 days
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check:
1/5 as many men will mow 1/5 the acres in the same time, so
2 men working for 5 hours a day for 6 days mow an area of 1 acre
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4 times as many men will mow 4 times the acres in the same time, so
8 men working for 5 hours a day for 6 days mow an area of 4 acres
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5 hours a day for 6 days = 30 hrs
4 hours a day for 7.5 days = 30 hrs
OK