SOLUTION: I'm a college grad and studying for the GMAT, and I'm having trouble solving word problems involving time, and unfortunately the pre-test software doesn't explain calculations to t
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Question 479833: I'm a college grad and studying for the GMAT, and I'm having trouble solving word problems involving time, and unfortunately the pre-test software doesn't explain calculations to their answers, so I'm at a loss and kind of embarrassed. For instance, "A company has two types of machines, type R and S, operating at a constant rate, a machine of type R does a certain job in 36 hrs and machine S does that same job in 18hrs. If the company used the same number of EACH TYPE machine to do the job in 2 hours, how many machines of EACH type were used?" The answer is six, but I don't understand the calculations or the computations that were used get this answer. Thanks.
Let n be the number of machines of each type that were used to
complete the job in only 2 hours.
Make this chart. (After you get the hang of how to do these
problems you may not need to do a chart, but make one anyway
to get the hang of it):
jobs hrs. rate in
done required jobs/hr
1 type R machine alone
1 type S machine alone
n type R machines together
n type S machines together
n type R's and n type S's
In each case 1 job was done, so fill in 1 for the jobs done in
all 5 cases:
jobs hrs. rate in
done required jobs/hr
1 type R machine alone 1
1 type S machine alone 1
n type R machines together 1
n type S machines together 1
n type R's and n type S's 1
We are told the no. of hours required in 3 of the cases.
We fill those in
jobs hrs. rate in
done required jobs/hr
1 type R machine alone 1 36
1 type S machine alone 1 18
n type R machines together 1
n type S machines together 1
n type R's and n type S's 1 2
Now we can fill in the rates in job/hr by dividing jobs by hours:
jobs hrs. rate in
done required jobs/hr
1 type R machine alone 1 36 1/36
1 type S machine alone 1 18 1/18
n type R machines together 1
n type S machines together 1
n type R's and n type S's 1 2 1/2
since 1 type R machine's rate is 1/36 jobs/hr, n type R machines
would have a rate n times as fast or n/36 jobs/hr. Similarly, n
type S machines would have a rate of n times as fast as 1/18 or
n/18 jobs/hr. Fill those in:
jobs hrs. rate in
done required jobs/hr
1 type R machine alone 1 36 1/36
1 type S machine alone 1 18 1/18
n type R machines together 1 n/36
n type S machines together 1 n/18
n type R's and n type S's 1 2 1/2
The equation comes from:
Multiply through by LCD = 36
Edwin
