document.write( "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.
\n" ); document.write( "Hint: 1m3 = 1000 liter.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #639050 by robertb(5830) $\"\"$ $\"About$

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 $\"0%3C=y%3C=2\"$ .
\n" ); document.write( "Taking derivatives of both sides wrt time t, we get\r
\n" ); document.write( "\n" ); document.write( " $\"dV%2Fdt+=+%2825%2F2%29%282y%29%28dy%2Fdt%29+=+25y%28dy%2Fdt%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Now $\"dV%2Fdt+=+0.3m%5E3%2Fmin\"$ , and so\r
\n" ); document.write( "\n" ); document.write( " $\"0.3+=+25%281.5%29%28dy%2Fdt%29\"$ ==> $\"0.3%2F37.5\"$ 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. \n" ); document.write( "

\n" );