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Three spraying machines working together can finish painting a house in $ 60 $ minutes. How long will it take for $ 5 $ machines of the same capacity to do the same job? (in minutes)

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Last updated date: 22nd Jul 2024
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Answer
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Hint: First of all we will find the total minutes required to work if instead of three machines one is used and then will use the ratio and proportion formula to find the time required in minutes if five machines are used.

Complete step-by-step answer:
Given that: Three spraying machines working together can finish painting a house in $ 60 $ minutes
Now, three machines worked for $ 60 $ minutes to paint a house
If single machine works it takes $ = 3 \times 60 $ minutes
Find the product of the above expression –
If single machine works it takes $ = 180 $ minutes
Now, if the same work to paint house is done by five machines, then the time taken will be
 $ = \dfrac{{180}}{5} $
Find the factors of the term in the numerator –
 $ = \dfrac{{18 \times 2 \times 5}}{5} $
Common factors from the numerator and the denominator cancel each other and therefore remove from the numerator and the denominator.
 $ = 18 \times 2 $
Find the product of the terms in the above expression –
 $ = 36 $ minutes
Hence, the $ 5 $ machines of the same capacity will take $ 36 $ minutes to paint the house.
So, the correct answer is “ $ 36 $ minutes”.

Note: Always remember in indirect proportion, when machines are increased the time taken will be decreased and in the same way if machines are reduced then the time taken to complete the work will increase. Be good in framing the equations since it is the base of the solution.