# I want to know how long will it take to fill the sink if afaucet can fill a sink in 5 minutes while a drain will empty the same sink in 8 minutes. If the faucet is turned on and the drain is left open

I want to know how long will it take to fill the sink if afaucet can fill a sink in 5 minutes while a drain will empty the same sink in 8 minutes. If the faucet is turned on and the drain is left open
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Martha Dickson
I wrote this as a function of fractions. If filling is treated as a positive value, broken into fifths (5 min per fill), and drainage is a negative value, broken into eighths, the equation looks like this:
$\frac{x}{5}-\frac{x}{8}=1$
Where the 1 is a full sink. Now, we solve for x:
$\frac{x}{5}×\frac{8}{8}-\frac{x}{8}×\frac{5}{5}=1⇒\frac{8x}{40}-\frac{5x}{40}=1$
$\frac{3x}{40}×40=1×40⇒3x=40$
$x=\frac{40}{3}=13\frac{1}{3}$