SOLUTION: A small grain combine can harvest 100 acres in 24 hours, a medium combine can do the same job in 18 hours, and a large combine can do the job in 12 hours. If all three combines are

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Question 1200128: A small grain combine can harvest 100 acres in 24 hours, a medium combine can do the same job in 18 hours, and a large combine can do the job in 12 hours. If all three combines are used at the same time, how long will it take to harvest 800 acres?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
First task could be, find the rate of all three machines working together.
WHICH MACHINE          RATE, acres per hours
small                   100/24
medium                  100/18
large                   100/12
All-Together       100/24+100/18+100/12


%283%2F3%29%28100%2F24%29+%2B+%284%2F4%29%28100%2F18%29+%2B+%286%2F6%29%28100%2F12%29
300%2F72%2B400%2F72%2B600%2F72
1300%2F72
325%2F18--------the rate of three-combined machines

800 acres, how much time?
%28325%2F18%29%2Ax=800

x=800%2818%2F325%29

44 hours 19 minutes

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The response from the other tutor shows a solution using the standard algebraic method, using the work rates of the three combines.

A different method usually makes for a solution using simpler calculations.

Consider the least common multiple of the three given times for harvesting 100 acres: 72 hours. In 72 hours...
the small combine can harvest 100*3 = 300 acres;
the medium combine can harvest 100*4 = 400 acres; and
the large combine can harvest 100*6 = 600 acres

So in 72 hours the three combines together could harvest 300+400+600 = 1300 acres; that means the time to harvest 800 acres is

ANSWER: (8/13)*72 hours = 576/13 hours or about 44.3 minutes.