SOLUTION: A farmer harvested 2400 ha of grain in 16 days using four machines. How long would it take to harvest 2400 ha if he used 6 machines?

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Question 1116571: A farmer harvested 2400 ha of grain in 16 days using four machines. How long would it take to harvest 2400 ha if he used 6 machines?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solution  1.   Counting machine-days: 

4 * 16 = 6 * x     (the number of machine-days should be the same in both cases)  ====>


x = %284%2A16%29%2F6 = 64%2F6 = 104%2F6 days = 102%2F3 days.


Solution  2.   Counting rate of work for one machine per day: 

2400%2F%284%2A16%29 = 2400%2F%286%2Ax%29     (<<<---=== saying that the rate of work is the same in both cases)


It leads you to the same equation as in solution 1:


4 * 16 = 6 * x  


which gives you the same answer  


x = %284%2A16%29%2F6 = 64%2F6 = 104%2F6 days = 102%2F3 days.

Solved.


Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


Solution 3, which I personally think is easiest and fastest:

The number of machines is 6/4 = 3/2 times as many, so the amount of time required is 2/3 as much:

16%2A2%2F3+=+32%2F3 or 10 2/3 days