Question

A swimming pool is to be drained for cleaning . If L represents the number of liters of water in the pool t seconds after the pool has been plugged off to drain and $L=200(10-t{)}^2$, how fast is the water running out at the end of 5s and what is the average rate at which the water flows out during the first 5s?

Answer 1

Let L represents the number of liters of water in the pool t second after the pool has been plugged off to drain, then
$L=200(10-t{)}^2$
$\therefore$ Rate at which water is running out = -$\frac{dt}{dt}\frac{dl}{dt}=-200.2(10-1).(-1)=400(10-t)$
Rate at which the water is running out at the end of 5 s
$=400(10-5)=2000L/s$
Since, initial rate $=-{\left(\frac{dL}{dt}\right)}_{t=0}=4000l/s$
$\therefore$ Average rate during $5s=\frac{initialrate+Finalrate}{2}=\frac{4000+2000}{2}=3000L/s$