Rate of painting problem

[orangepopsicle]

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Hello,

I am having trouble understanding the thought process that goes behind how to solve this problem. i know 1/T1 + 1/T2 etc = 1/T for when everybody is working together with their different rates. But do not know how to incorporate that into this question:

James can paint a room in 4 hours, while Mike can paint the same room in 5 hours. Working together, how many hours will it take them to paint the room if James only works for one hour?

 

[Typical Average Student]

http://forums.studentdoctor.net/threads/math-destroyer-test-2-question-13-2014-edition.1107144/

 

[DAT Destroyer]

Hello,

I am having trouble understanding the thought process that goes behind how to solve this problem. i know 1/T1 + 1/T2 etc = 1/T for when everybody is working together with their different rates. But do not know how to incorporate that into this question:

James can paint a room in 4 hours, while Mike can paint the same room in 5 hours. Working together, how many hours will it take them to paint the room if James only works for one hour?

There are 2 ways to do these type of problems. here's the easy way first:

start with the person that leaves after one hour ( James )
you should know : Job = Rate x Time

Job = (1/4)x(1). because James can the entire job in 4 hours his rate is 1/4. Meaning he can do 1/4 thof the job in one hour.

Job = 1/4
now job left to do is 1-1/4 = 3/4

Mike:
Job = Rtae x Time
3/4 = (1/5)x t. solve for t to get : t = 3 3/4 and that's your answer

The other way to do it is find how much of a job they both did in one hour

job = (1/4 + 1/5)x 1 = 9/20. You add both rates
job left is 1-9/20 = 11/20

now Mike:

11/20 = (1/5)x t
solve for t to get 11/4. BUT remember to ass the one hour they worked togother

11/4 + 1 = 15/4 = 3 3/4

Hope this helps.

 

[orangepopsicle]

Since they were both working in the first hour, why would the first hour only be defined by the work James did? Wouldn't it be a culmination of both James and Mike's rates for the first hour, then just Mikes rate for the job that is left?

 

[MolarDentist]

I believe because they worked together that hour has already taken into consideration. I did the same problem the second way. It's longer but I got the same answer.

 

[510586]

Since they were both working in the first hour, why would the first hour only be defined by the work James did? Wouldn't it be a culmination of both James and Mike's rates for the first hour, then just Mikes rate for the job that is left?

Since James only did it for one hour his entire contribution is already taken into account when we say 1/4 hours of the wall has been painted in one hour. Mike painting .75 of the wall includes the first hour painting with Jim. It's just that we removed Jim from the equation because we know how much he painted in that time