Chapter 7.8, Problem 23P

To determine

Tofind:the duration of each pipe to fill the pools.

Answer to Problem 23P

largest pipes took $5\frac{1}{2}$ hours to fill the pools by itself.

Smallest pipe took $16\frac{1}{2}$ hours to fill the pool by itself.

Others pipe took $\text{11}$ hours to fill the pool by itself.

Explanation of Solution

Given:

The largest pipe alone takes one third the smallest pipe and half the time other pipe takes.

Concept used:

Rate of the work:

Ratio of work to the time interval with changes in time rate of work will change.

  $\text{work rate=}\frac{\text{work done}}{\text{time}}$ .

  $\text{work rate}\times \text{time=workdone}$ .

Calculation:

The equation where $\text{x}$ is how long it take the largest pipe to fill the pool on its own.

So, the smallest pipe takes $\text{3x}$ hours and other pipe takes $\text{2x}$ hours.

  $\frac{\text{3}}{\text{x}}\text{+}\frac{\text{3}}{\text{3x}}\text{+}\frac{\text{3}}{\text{2x}}\text{=1}$ .

Multiplying both side by the L.C.D of $\text{6x}$ :

  $\text{18+6+9=6x}$

Combining like terms:

  $\text{6x=33}$ .

Dividing both sides by $\text{6}$ :

  $\text{x=}\frac{11}{2}=5\frac{1}{2}$ .

Finding the rate of other two pipes:

  $\text{2x=2×}\frac{\text{11}}{\text{2}}\text{=11}$ and $\text{3x=3}\times \frac{11}{2}=\frac{33}{2}=16\frac{1}{2}$ .

Hence,

1. largest pipes took $5\frac{1}{2}$hours to fill the pools by itself.
2. Smallest pipe took $16\frac{1}{2}$ hours to fill the pool by itself.
3. Others pipe took $\text{11}$ hours to fill the pool by itself.