Left on together the cold and hot water faucets of a certain

Left on together, the cold and hot water faucets of a certain bathtub take 7

minutes to fill the tub. If it takes the hot water faucet 17 minutes to fill the tub by itself, how long will it take the cold water faucet to fill the tub on its own?

Do not do any rounding.

Solution

Let h = the time required by the hot faucet to fill the tub.

Let the full tub = 1.

Cold water faucet takes 17 minutes to fill the tub .

In one minute cold water will fill 1/17 of the tub.

Similarly hot water faucet will fill 1/h of the tub in one minute .

If it take 7 minutes by both faucets to fill the tub ,then in one minte 1/7 of the tub will be filled

thus we can write
tub filled by cold water faucet in one minute +tub filled by hot water faucet in one minute= tub filled by both faucet in one minute
1/17 + 1/h = 1/7
multiply both sides by 7
7/17+ 7/h = 1
take 17h as common denominator
7h + 7(17) = 17h
7h + 119 = 17h
119 = 17h - 7h
119 = 10h
h = 119/10
h = 11.9 min for the hot water to fill it