SOLUTION: A rectangular swimming pool 10 m long and 5 m wide has a depth of 3 m at one end and 1 m at the other end. If water is pumped into the pool at the rate of 300 litres per minute, at

Question 1023420: A rectangular swimming pool 10 m long and 5 m wide has a depth of 3 m at one end and 1 m at the other end. If water is pumped into the pool at the rate of 300 litres per minute, at what rate is the water level rising when it is 1.5 m deep at the deep end.
Hint: 1m3 = 1000 liter.

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
By using similarity of triangles, the volume of the triangular prism will be , where y is the height of the pool, and .
Taking derivatives of both sides wrt time t, we get

Now , and so
==> m/min = 0.008 m/min = dy/dt, the rate at which the water level is rising when it is 1.5 m deep at the deep end.
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