How long will it take Paul to do it alone?

Question

Working together, Paul and Daniel can pick forty bushels of apples in 4.95 hours.  Had he done it alone it would have taken Daniel 9 hours.

Answer 1

In dealing with questions of this sort we set up an

equation dealing with "parts per hour" each can do.

If p = # hours it takes Paul to do the job alone then

Paul completes 1/p parts per hour...

By the same logic Daniel completes 1/d parts per hour

 

Add the parts per hour completed by both and multiply

that sum by the number of hours it takes them to do it

together ... that sum equates to 100% of the job or .. 1

 

h(1/p + 1/d) = 1

 

h = 4.95

d = 9

 

4.95(1/p + 1/9) = 1

divide both sides by 4.95

1/p + 1/9 = 1/4.95

subtract 1/9 from both sides

1/p = 1/4.95 - 1/9

common denominator or right of (4.95)(9) 

1/p = (9-4.95)/((4.95)(9))

1/p = 4.05/44.55

 

p = 44.55/4.05 = 11

 

It takes Paul 11 hours working alone