word problem

Question

A sink has two faucets: one for hot water and one for cold water. The sink can be filled by a cold water faucet in
4.5
minutes. If both faucets are open, the sink is filled in
3.6
minutes. How long does it take to fill the sink with just the hot water faucet open?

Answer 1

The cold faucet does 3.6/4.5 of the job.

The hot faucet does 0.9/4.5 of the job.

Working alone the hot faucet needs 5 minutes - 5 (0.9/4.5) = 1

Answer 2

V = Volume

FRH = Faucet Rate Hot

FRC = Faucet Rate Cold

 

V = FRC * T

V = FRC * 4.5

FRC = V / 4.5

 

V = (FRC + FRH) * 3.6

V = (V/4.5 + FRH) * 3.6

V = 4/5 V + FRH * 3.6

1/5 V = FRH * 3.6

V = 18 FRH

 

FRC * 4.5 = 18 FRH

FRC = 4 FRH

 

FRH = FRC / 4

 

FRH is 1/4 as fast as FRC

 

if it takes 4.5 minutes to fill with FRC, it will take 18 minutes to fill with FRH