Question

Mike can pick forty bushels of apples in 14 hours. One day his friend John helped him and it only took 6.16 hours. Find how long it would take John to do it alone.

A) 20 hours

B) 7 hours

C) 9.4 hours

D) 11 hours

Answer 1

To find how long it would take John to pick 40 bushels of apples alone, we can use the concept of work rates. By subtracting Mike's work rate from the combined work rate of Mike and John, we can find John's work rate. Dividing the total number of bushels by John's work rate gives us the time it would take John to pick the apples alone.

Step-by-step explanation:

To find out how long it would take John to pick forty bushels of apples alone, we can use the concept of work rates. We know that Mike takes 14 hours to pick forty bushels of apples, so his work rate is 40 bushels / 14 hours = 40/14 bushels per hour. When Mike and John work together, they can complete the task in 6.16 hours, so their combined work rate is 40 bushels / 6.16 hours = 40/6.16 bushels per hour.

To find John's work rate, we can subtract Mike's work rate from the combined work rate: 40/6.16 - 40/14 = 40(1/6.16 - 1/14) = 40(7/43.04 - 3.08/43.04) = 40(3.92/43.04) = 3.67 bushels per hour.

Finally, to find out how long it would take John to pick the forty bushels of apples alone, we can divide the total number of bushels by John's work rate: 40 bushels / 3.67 bushels per hour = 10.9 hours.