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 $L=200(10-t{)}^2$. What is the average rate at which the water flows out during the first $5$ seconds $\left(\frac{litres}{sec}\right)$?

Answer 1

$L={200(10-t)}^{2}L=200(100+t^2-20t)\frac{dL}{dt}=200(2t-20)=400(t-10t)$

Average for first five sec$=\frac{400}{6}{\sum }_{t=0}^5(t-10)=\frac{400}{6}\times (10+9+8+7+6+5)=3000l/s$