1. ## Problem

Hi
Here is my problem:

If the hot water faucet is left on alone, it takes 20 minutes to fill the bathtub. It takes only 15 minutes to fill the bathtub if the cold water faucet is left on alone. It takes 12 minutes to fill the bathtub if both faucets are left on and the drain is open. How long will it take to drain a full bathtub?

The answer is 30 minutes, but I don't know how to get that. Any help would be appreciated. Thanks.

2. Originally Posted by Averee
Hi
Here is my problem:

If the hot water faucet is left on alone, it takes 20 minutes to fill the bathtub. It takes only 15 minutes to fill the bathtub if the cold water faucet is left on alone. It takes 12 minutes to fill the bathtub if both faucets are left on and the drain is open. How long will it take to drain a full bathtub?

The answer is 30 minutes, but I don't know how to get that. Any help would be appreciated. Thanks.
Use my formula as a hint.

If it takes one thing to do work in A hours (or seconds whatever).
And another thing to do the same work in B hours.

Then together it shall take,
AB/(A+B)

3. AB/(A+B)

So

20 x 15 / (20 + 15)
= 300 / 35
= 8.57

???

4. Originally Posted by Averee
Hi
Here is my problem:

If the hot water faucet is left on alone, it takes 20 minutes to fill the bathtub. It takes only 15 minutes to fill the bathtub if the cold water faucet is left on alone. It takes 12 minutes to fill the bathtub if both faucets are left on and the drain is open. How long will it take to drain a full bathtub?

The answer is 30 minutes, but I don't know how to get that. Any help would be appreciated. Thanks.
Hello, Averee,

A is the amount of hot water per minute
B is the amount of cold water per minute
T is the amount of water if the tub is filled.

Then you know
20*A = T ==> A = 1/20*T
15*B = T ==> B = 1/15*T

x is the amount of water per minute which will leave the tub if the drain is open.

Then you know:

12*A + 12*B - x = T . Plug in the values for A and B:
12*(1/20)*T + 12*(1/15)*T - x = T
(7/5)*T - x = T
x = 2/5*T. That means: In 12 minutes 2/5 of the contents of the tub is running out:
2/5*T = 12 min ==> T = 60/2 min = 30 min

PS.: We assume here that the speed of the water is constant when it is running out of the tub. Actually the speed depends on the pressure and the pressure depends on the level of water. So the speed will decrease if only a little bit water is left.