Question

A water filter takes $ 40 $ minutes to filter $ 20 $ litres of water. Another filter of the same specifications takes $ 30 $ minutes to filter the same amount of water. If both the filters are used at the same time. Then how long will it take them to filter the $ 70 $ litres of water?

Answer 1

Hint: First of all we will understand the given data, and then find out the speed of the water filtered per minute for both the water filters. Use the formula of the water filtered in litres per time taken in minutes.

Complete step-by-step answer:
Here we are given two water filters.
First filter takes $ 40 $ minutes to filter $ 20 $ litres of water.
Therefore, water filtered in $ 1 $ minutes is $ = \dfrac{{20}}{{40}} $ litres per minute
Now simplify the above fraction, removing the common factors from the numerator and the denominator.
Hence, the water filtered by the first filter in $ 1 $ minutes is $ = \dfrac{1}{2} $ litres per minute …… (A)
Now, water filtered by the second filter, $ 30 $ minutes to filter $ 20 $ litres of water.
Therefore, water filtered in $ 1 $ minutes is $ = \dfrac{{20}}{{30}} $ litres per minute
Now simplify the above fraction, removing the common factors from the numerator and the denominator.
Hence, the water filtered by the second filter in $ 1 $ minutes is $ = \dfrac{2}{3} $ litres per minute …… (B)
Both the filters are used together, so they can filter water in one minute
 $ = \dfrac{1}{2} + \dfrac{2}{3} $
Simplify the above expression –
 $ = \dfrac{7}{6} $ litres
Now, if $ \dfrac{7}{6} $ litres can be filtered in one minute, then
 $ 70 $ litres of water can be filtered in
 $ = \dfrac{{70 \times 1}}{{\dfrac{7}{6}}} $
 $ = \dfrac{{70 \times 6}}{7} $
 $ = 60 $ minutes
The sixty minutes means one hour.
Hence, if both the filters are used together then it will take one hour.
So, the correct answer is “ $ 60 $ minutes ”.

Note: Understand the word problem properly and perform a step by step approach to get the speed of one filter, second filter and the speed of both the filters together. Be good in multiples and division and remember that the common factor from the numerator and the denominator cancels each other.