Question

Three pumps of the same capacity can fill a swimming pool in $15$ hours. How long will it take for $5$ pumps of the same capacity to fill the pool?

Answer 1

Hint: We are provided with the data of different numbers of pumps which can fill a swimming pool of the same capacity. We know that the time to fill is always inversely proportional to the number to pumps used to fill the pool which can be written as:
Time=k/number of pumps used
It becomes $t = \frac{K}{p}$ where, $K$ is the constant.
We can solve for the constant by given data and then put the value of constant to find the time for $5$ pumps.

Complete step-by-step answer:
From the question, we know three pumps of the same capacity can fill a swimming pool in $15$ hours.
So, the time relation to number of pumps used is:
 $t = \dfrac{K}{p}$
In the above equation, we have time $15$ hours and $3$ pumps are there to fill the swimming pool.
So,
 $
\Rightarrow t = \dfrac{K}{p} \\
\Rightarrow 15 = \dfrac{K}{3} \\
\Rightarrow K = 3 \times 15 \\
\Rightarrow K = 45 \\
 $
Now, we have to calculate the time taken by 5 pumps of the same capacity to fill the swimming pool.
Using the above equation,
 $
\Rightarrow t = \dfrac{{45}}{5} \\
\Rightarrow t = 9 \\
 $
Therefore, it will take $9$ hours to fill the swimming pool by using $5$ pumps of the same capacity.

Note: The constant in the time relation is inverse proportionality constant which is same for all the same capacity data. We can also calculate simply by taking the proportionality of number of hours and number of pumps used. The alternate method is:
Product of extremes=product of means
Let us assume $15$ pumps can take time $t$
 $
\Rightarrow \dfrac{3}{5} = \dfrac{{15}}{t} \\
\Rightarrow 3 \div 5 = 15 \div t \\
\Rightarrow t = 9 \\
 $
The time required is the same which is $9$ hours.