SOLUTION: Please help with the following rate question? Ian can remodel a kitchen in 20 hours and Jack can do the same job in 15 hours. if they work together, how many hours will it take t

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Question 1037504: Please help with the following rate question?
Ian can remodel a kitchen in 20 hours and Jack can do the same job in 15 hours. if they work together, how many hours will it take them to remodel the kitchen?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
Their combined rate is the sum of their individual rates. The rates need to be as KITCHEN/HOURS, or as JOB/HOURS.
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
Please help with the following rate question?
Ian can remodel a kitchen in 20 hours and Jack can do the same job in 15 hours.
if they work together, how many hours will it take them to remodel the kitchen?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Since Ian can complete the job in 20 hours, he makes  of the job in one hour. It is Ian's rate. It is measured in job-per-hour units.

Since Jack can complete the job in 15 hours, he makes  of the job in one hour. It is Jack's rate. 

If Ian and Jack work together, they make  =  =  of the entire job in an hour (in each hour). 


(When two workers work together, their rates add up. Their combined rate is the sum of the individual rates.)


Hence, they need  =  hours to complete the job, if they work together.

It is a typical problem on joint work.
For a variety of similar solved joint-work problems see the lesson
Using fractions to solve word problems on joint work in this site,
and also associated lessons.


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