Combining work rates (other ways to solve these problems?)

Question

How do you solve the fractional expression in the first problem? 
What other ways are there to solve this type of problem?

Q: If Tom can do a job in 10 hours and Tom and Mary can do the job in 6 hours working at their respective rates, how long will it take Mary to do the job by herself.

I know of two possible ways to solve this.

(1) Using the (X*Y)/(X+Y) formula I came up with:

 (10*M)/(10+M) = 6 
 
Where T=X=10 and Y=M. And because my math skills are rusty I don't know where to go from here. Am I cross multiplying the fractional expression?

(2) Using the Princeton method of pie charts:

 Tom =  w=120 
 r=12/hr | t=10hrs


 Tom and Mary =  w=120 
 r=10 + M? | t=6hrs 


 Mary =  w=120 
 r= 10/hr | t= 12hrs

I got the question right after plugging in any Work value that is a multiple of 6 and 10; 60, 120, etc.

nocilis · Answer

Rate problems can be tackled easily, if you follow a method.
A simple way to do Rate problems is to use the following formula:

X1/T1 + X2/T2 = J

X1= Time spent together by A
X2 = Time spent together by B
T1 = Time spent alone by A
T2 = Time spent alond by B
J= Fraction of job

Here, X1 =6, X2= 6, T1=10, T2 = unknown, J= 1 (full job)
=> T2 = 15
(This problem could be solved in about 30 second with this method).
This formula can be used for almost all rate problems, including the one that involves many people once you think through the problem and obtain the correct parameters to plug it into the above equation. In GMAT this will help in terms of time!

See another rate problem that is solved easily using this formula at https://www.gmatclub.com/phpbb/viewtopic.php?t=13304

rxs0005 · Answer

my advice to u is work leess on the formula undrstand the concept of rate and work that will help u and tackle complicated problmes . cuz GMAT Will not give u straight forward problomes where u can plug numbers in a formula 

work on fundamentals it may take time but it will stick in your brain!! 

thts my opinion

HongHu · Answer

Let say Tom's working rate is t and Mary's working rate is m.

10t=6(t+m)
4t=6m
=>10t=15m

In other words, the work that Tom can finish in 10 hours, Mary will need 15 hours to finish it.

It's quite similar to distance problem, actually.

Folaa3 · Answer

Here is another approach:

Tom can do a job in 10 hours means he doesn 1/10 of the job in an hour

Tom and Mary can do the same job in 6 hours means they both can get 1/6 of the job done in an hour. 

To find Maryâ€™s rate (M), then the sum of their rate per hour = their rate combined per hour.

1/10 + 1/M = 1/6. 
1/M = 4/60 (note that this is the time it takes marry per hour)
Take the reciprocal of this fraction and you will get the time it takes marry to complete the same job alone = 60 / 4 = 15 hours.

I hope that helps.

mbk5w · Answer

Nocilis, could you give an example using your method of solving?

scorer · Answer

1/T + 1/M = 1/6

1/10 + 1/M = 1/6

1/M = 1/6-1/10
1/M = 4/60 = 1/12

M = 12 hr

scorer · Answer

oops! i mean M=15 hr.

texaspunk · Answer

HEllo HH, I am trying to learn all the different methods to solve this, but I missed a step in your solution.

How did you go from: 4t=6m to 10t=15m
ThanksTP

halahpeno · Answer

10t=6(t+m)
4t=6m
t=1.5m

Here, you get the ratio of Tom's work to Mary's work. Knowing that Tom takes 10 hours, you plug that in to the ratio and get 15 for Mary.

I would probably go about it like Folaa3 does... I usually figure out how much of a job each can do in an hour...

HongHu · Answer

halahpeno is right. Though I would try to avoid fractions and/or decimals in the test to save time. So what I'd do is this: 4t=6m 2t=3m (divided both sides by 2) 10t=15m (multiply both sides by 5)

Combining work rates (other ways to solve these problems?)

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