Answer:
Given:
Cold water faucet fills the sink in 4 minutes.
Both faucets fills the sink in 3 minutes.
Let us assume that "t" be the time it takes hot water faucet in order to fill the sink.
Therefore;
Rate for hot water faucet fills the sink = [tex]\frac{1}{time}[/tex] = [tex]\frac{1}{t}[/tex]
Rate at which cold water faucet fills the sink = [tex]\frac{1}{time}[/tex] = [tex]\frac{1}{4}[/tex]
When both faucets are used , the rate at which they fill the sink is given as :
[tex]\frac{1}{t}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{3}[/tex]
On solving the above equation, we get :
[tex]4t = 3t +12[/tex]
∴ [tex]t = 12\ minutes[/tex]
Therefore, it takes 12 minutes for the hot water faucet to fill the sink.
