Chapter 6.3, Problem 41E

To determine

To find: The average rate at which the water released.

Answer to Problem 41E

The average rate at which the water released is $\frac{40}{3}{\text{m}}^3/\text{min}$

Explanation of Solution

Given information :

Volume of water released by dam = $1000m^3$

Rate at which water is released = $10m^3/min$ .

Volume of water released by dam next time = $1000m^3$

Rate at which water is released = $20m^3/min$

Calculation :

Time taken is calculated by ratio of volume of water divided by rate in each case. Then add both to calculate total time.

  $\begin{array}{cc}\text{total time taken}& =\frac{1000}{10}+\frac{1000}{20}\\ & =100+50\\ & =150\text{minutes}\end{array}$

So,

  $\begin{array}{cc}\text{average rate}& =\frac{\text{total water released}}{\text{total time taken}}\\ & =\frac{1000+1000}{150}\\ & =\frac{2000}{150}\\ & =\frac{40}{3}{\text{m}}^3/\text{min}\end{array}$