Solving a work problem using a rational equation

Question

It takes the cold water faucet twice as long to fill a bathtub as it does the hot water faucet. Left on together, the cold and hot water faucets take 5  minutes to fill the tub. How long will it take the hot water faucet to fill the tub by itself?

Answer 1

1/2x + 1/x = 1/5

3/2x = 1/5

2x = 15

x = 15/2 = 7.5 minutes for the hot water faucet to fill the tub alone

cold water faucet take 15 minutes to fill it alone

1/15 + 1/7.5 = 1/15 + 2/15 = 3/15 = 1/5