Question

With both taps open, Blake can fill his kitchen sink in 6 minutes. When full, the sink drains in 10 minutes. How long will it take to fill the sink if Blake forgets to put in the stopper?

Answer 1

The time to fill the sink if Blake forgets to put in the stopper would be 15 mins.

Step-by-step explanation:

Given that,

The kitchen sink can fill in: 6 mins

The sink can drain in: 10 mins

We have to find the time to fill the sink if Blake forgets to put in the stopper. For that,

Lets say, the full tank = 1

Filling rate = $\frac{x}{6}$

Drainage rate = $\frac{x}{10}$

Hence, the time to fill the tank would be:

$\frac{x}{6} - \frac{x}{10} = 1$

$30.\frac{x}{6} - 30.\frac{x}{10} = 30.1$  (Multiply by LCM)

$5x - 3x = 30$

$2x = 30$

x = 15

Hence, the time to fill the sink if Blake forgets to put in the stopper would be 15 mins.