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 = [tex]\frac{x}{6}[/tex]
Drainage rate = [tex]\frac{x}{10}[/tex]
Hence, the time to fill the tank would be:
[tex]\frac{x}{6} - \frac{x}{10} = 1[/tex]
[tex]30.\frac{x}{6} - 30.\frac{x}{10} = 30.1[/tex] (Multiply by LCM)
[tex]5x - 3x = 30[/tex]
[tex]2x = 30[/tex]
x = 15
Hence, the time to fill the sink if Blake forgets to put in the stopper would be 15 mins.
