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

Algebra ->  Volume -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
By using similarity of triangles, the volume of the triangular prism will be V+=+%2825%2F2%29%2Ay%5E2, where y is the height of the pool, and 0%3C=y%3C=2.
Taking derivatives of both sides wrt time t, we get
dV%2Fdt+=+%2825%2F2%29%282y%29%28dy%2Fdt%29+=+25y%28dy%2Fdt%29
Now dV%2Fdt+=+0.3m%5E3%2Fmin, and so
0.3+=+25%281.5%29%28dy%2Fdt%29 ==> 0.3%2F37.5m/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.