Question 1095618
If the main pump is started at 5 and it runs until 9, then the problem is telling us the main pump will run 4 hours, so we just need to find out how long the auxiliary pump has to run, I'll call this x:
Main pump can empty tank in 5 hours but will run 4 and 4 out of 5 = 4/5
Add the time the auxiliary pump will run, it will run x hours and could empty the tank by itself in 14: x/14 Add the two together:
4/5 + (x/14) = 1
x(1/14) = 1 - 4/5
x(1/14) = 1/5
x = 1/5(14)
x = 2.8 hours = 2(.8*60) = 2hours 48 minutes. This is how long the auxiliary pump has to run in order for the two pumps to empty the tanker by 9. Subtract 2h 48min from 9 to get your answer.