Hi All,
These types of rate questions can be solved in a few different ways. Since the prompt discusses how two machines will work together on a task, you can use the Work Formula. By TESTing VALUES, we can come up with a simple example that will answer the given question.
We're told that:
1) Machine X can do a job in HALF the time that it takes Machine Y
2) Machine Z takes 50% longer to the do the job than Machine X
Since Machine X appears in both 'facts', we want to TEST a VALUE for X that is easily doubled AND halved....
X = 2 hours to complete the job
With that value in place, we can figure out the other 2 values....
Y = 4 hours to complete the job
Z = 3 hours to complete the job
We're asked for the ratio of the time it takes (X and Z) working together vs. the time it takes (Y and Z) working together.
The Work Formula: (A)(B)/(A+B)
For Machines X and Z, we have: (2)(3)/(2+3) = 6/5 hours to complete the job
For Machines Y and Z, we have: (4)(3)/(4+3) = 12/7 hours to complete the job
The ratio 6/5 : 12/7 needs to be "clean up" a bit. Since we're dealing with fractions, we can use common denominators....
6/5 : 12/7
42/35 : 60/35
Now we can eliminate the denominators...
42 : 60
And reduce the ratio....
7 : 10
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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