Chapter 11.5, Problem 39PPE

To determine

To find the time taken to fill the tank by larger pipe alone, also tell the variable in which given situation should be defined, and write the fraction of tank filled in 1 hour by the larger pipe alone and by smaller pipe alone.

Answer to Problem 39PPE

Time taken by larger pipe alone is $\frac{9}{4}$ hours.

Time taken to fill the tank by smaller pipe alone is $\frac{27}{4}\text{ hours}$ .

Variable x is used to define the time taken by larger pipe to fill the tank alone.

Explanation of Solution

Given:

Time taken to fill the tank is 9 hours.

Time taken by smaller pipe is three times as the time taken by the larger pipe.

Calculation:

To find the time taken to fill the tank by larger pipe alone first define the given situation using a variable.

Since, time taken by smaller pipe is three times as the time taken by the larger pipe, that means if the time taken by the larger pipe is x , then time taken by the smaller pipe is 3x

Now, the total time taken by the both pipes to fill the tank is 9 hours that means

  $\begin{array}{c}x+3x=9\\ \Rightarrow 4x=9\\ \Rightarrow x=\frac{9}{4}\text{ hours}\end{array}$

Thus, time taken by larger pipe alone is $\frac{9}{4}$ hours. And time taken to fill the tank by smaller pipe alone is

  $3\times \frac{9}{4}=\frac{27}{4}\text{ hours}$