Question

How do you set up this problem?
A pump can empty a small pond in 4 hours. Another more efficient pump can do the job in 3 hours. How long would it take to empty the pond if both pumps were used?

Answer 1

First off, you know it will be less than 3 hours. Use product over sum.
(4 X 3)/7
12/7
1 5/7 hour if you want to convert to minutes , go ahead.

Answer 2

Thank you!

Answer 3

There is another way to work it, where 1/4 + 1/3=1/combined pump time
3/12 + 4/12= 1/x
1/4 is amount pumped in 1 hour
1/3 is amount pumped in 1 hour
combined (add) is the amount the combined pumps in 1 hour.

Answer 4

Multiply thruy by 12 getting 3+4=12/x
7/1 = 12/x or 7x=12, x=12/7

Answer 5

Same answer, product over sum is the way to go.

Answer 6

If there were more than 2 pumps say 3, then do two using product over sum, and then use the result with the remaining one using product over sum.