Question

For a certain bathtub, it takes the hot water faucet
3
times as long to fill the tub as it does the cold water faucet. Left on together, the two faucets take
6
minutes to fill the tub. How long will it take the hot water faucet to fill the tub by itself?

Answer 1

9 minutes?

Answer 2

No

Answer 3

Let c= the flow rate for cold water (tub/min)

We are given that the flow rate for hot water is 1/3 of the cold water rate.

So we have this equation.

1/3c + c = 1tub/6 minutes

4/3c = 1/6
c= 1/6*3/4
c=3/24
c=1/8 or 1 tub/8 minutes

So the cold water faucet can fill the tub by its self in 8 minutes.

The hot water flow rate is 1/3 of the cold water rate.

So 1/3 of 1/8 equals 1/24 or 1 tub/24 minutes

So the hot water faucet can fill the tub by its self in 24 minutes.

Check:

(1tub/24minutes) (6 minutes) + (1 tub/8minutes)(6 minutes) = 6/24 tub + 6/8 tub

6/24 tub + 18/24 tub = 24/24 tub or 1 tub