# Math

Two faucets can fill a tank in 1 hour and 20 minutes. The first faucet takes more than two hours longer to fill the same tank when functioning without the second tap. How long does it take to fill each one separately? Explain your solution

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1. time needed by 2nd faucet alone --- t hrs
rate for 2nd faucet alone = 1/t

time needed by 1st faucet alone --- t+2 hrs
rate of 1st faucet along = 1/(t+2)

combined rate = 1/t + 1/(t+2)
= (t+2 + t)/(t(t+2) = (2t+2)/(t(t+2))

then 1/[ 2t+2)/(t(t+2)) ] = 4/3
t(t+2)/(2t+2) = 4/3
3t^2 + 6t = 8t + 8
3t^2 - 2t - 8 = 0
(t-2)(3t+4) = 0
t = 2 or t = a negative time

the 2nd faucet would take 2 hours alone
the 1st facucet would take 4 hours alone

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