Nancy can clean her room in 2 hours. It takes her brother Sam 3 hours to complete the same task. How long will it take them if they worked together to get the room cleaned?
Answer: 6/5 hours
Steps to solve the problem:
This problem can be solved when we assume that both Nancy and Sam are working at a constant rate which means that each of them does the same amount of work in the first hour as they do in the last hour.
To try and find the total hours it takes both of them, we must find how much work can each one of them do in 1 hour. Therefore if Nancy completes the cleaning job in 2 hours therefore in 1 hour she completes 1/2 of the work. Also, if Sam completes the job in 3 hours, then in 1 hour he completes 1/3 of the work.
If we let x = the total number of hours it takes for both of them working together, then in 1 hour, they must do 1/x of the time.
Lets put everything together as follows:
Amount of work done by Nancy = 1/2
Amount of work done by Sam = 1/3
Total amount of work = 1/x
Lets add the hours to get the total as follows:
1/2+1/3 = 1/x
The lowest common denominator is 6x. Therefore, both sides of the equation are multiplied by 6x as follows:
6x (1/2) + 6x (1/3) = 6x (1/x)
3x + 2x = 6
5x = 6
x = 6/5 = 1.2 hours
It will take them 6/5 or 1.2 hours to get the room cleaned together.
©Copyright 2007.Najwa S. Hirn. All rights reserved.
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