Question

For a certain bathtub, the cold water faucet can fill the tub in 7 minutes. The hot water faucet can fill the tub in 13 minutes. If both faucets are used together, how long will it take to fill the tub?
Do not do any rounding.

Answer 1

Let's assign the variable x to represent the time it takes to fill the tub when both faucets are used together.

The rate at which the cold water faucet fills the tub is 1/7 tub/minute.
The rate at which the hot water faucet fills the tub is 1/13 tub/minute.

When both faucets are used together, the rates add up, so the equation becomes:

1/7 + 1/13 = 1/x

Multiplying by 91x to clear the fractions:

13x + 7x = 91

20x = 91

x = 91/20

Therefore, it will take approximately 4.55 minutes to fill the tub when both faucets are used together.