work word problem

Question

Working together, Willie and Rob can pick 40 bushels of apples in 6.74 hours. Had he done it alone, it would have taken Rob 14 hours. Find how long it would take Willie to do it alone.

Answer 1

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Answer 2

 

Hi.  You need to find the rate per hour for the two of them working together, Rob working alone, and Willie working alone.

 

First, together, the rate per hour is 40 bushels / 6.74 hours = 5.94 bushels per hour.

Rob alone, the rate per hour is 40 bushels / 14 hours = 2.86 bushels per hour.

Willie alone, the rate per hour is 40 bushels / x hours = (5.94-2.86) bushels per hour, since Willie would be picking the DIFFERENCE of the two of them working together (5.94) and Rob working alone (2.86).

 

Solving 40 / x = 3.08

 

  40 = 3.08x

  40 / 3.08 = x

  12.99=x

 

So it would take Willie 12.99 hours to pick 40 bushels.