# Algebra

2 pumps can fill a water tank in 45 minutes when working together. Alone, the second pump takes 3 times longer than the first to fill the tank. How long does it take the first pump alone to fill the tank?
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1. rate = job/time
let the time of the faster pump be t min
let the time of slower pump be 3t min

rate of slower = job/(3t)
rate of faster = job/t
combined rate = job/(3t) + job/t
= (job + 3job)/(3t) = 4job/(3t)

time working together = job/(4job/3t)) = 45
job(3t)/(4job) = 45
3t/4= 45
t = 60

Using only the first pump would require 60 minutes.

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