Three pumps can empty a 30-gallon tank in 45 minutes. How many pumps are required to empty a 120-gallon tank in 1 hour?

Question

I know what the answer is to this question (9) but I don't understand how to build a rate equation around this question so that I might answer similar questions in the future.

Answer 1

3 pumps empty 30 gallons in 45 minutes= 3/4 hr.

how many pumps empty 120 gallons in 60 minutes= 1 hour?? 9 pumps do the trick

answer to question (9) is 9. Ironic coincidence. questions are dressed to the nines, all nine yards

pumps vary inversely with time, directly with tank size

3 pumps do 30 gallons in 3/4 hour

that means

1 pump does 30/3=10 gallons in 3/4 hour

12 pumps do 120 gallons in 3/4 hour

1 pump does 10(4/3) = 40/3 gallons in 1 hour

9 pumps do 9(40/3) = 120 gallons in 1 hour