Working alone,Maria can pick forty bushels of apples in 10 hours.Kathryn can pick the same amount in 13 hours.Find how long it would take them if they worked together.  

Round your answer to the nearest hundredth.
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1 Answer

Maria works at the rate of 40 bushels per 10 hours=40/10=4 bushels per hour.

Kathryn’s rate is 40/13 bushels per hour.

Combined rate is 4+40/13=92/13 bushels per hour. This is the same as 13/92 hours per bushel.

So, for 40 bushels the time it takes is 40×13÷92=10×13/23=130/23=5.65 hours.

Another way to do this is to divide the 40 bushels in the ratio of their rates of working. Since they are both timed on how long it takes to pick 40 bushels, the ratio is 10:13. That means the quantity is split as 10/(10+13)=10/23 and 13/(10+13)=13/23. So 40 bushels is split as 10/23×40=400/23 bushels and 13/23×40=520/23 bushels.

The faster worker is given the larger portion. Maria is faster than Kathryn and her rate is 40/10=4 bushels per hour. The time it takes Maria to pick 520/23 (the larger portion) is quantity/rate=520/23÷4=130/23=5.65hrs approx. The time it takes Kathryn to pick 400/23 bushels at the rate of 40/13 bushels per hour is 400/23÷(40/13)=400/23×13/40=130/23=5.65hrs, the same time Maria takes to pick her portion.

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