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Ali and Moe can do a certain job together in 4 hours...

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Ali and Moe can do a certain job together in 4 hours...

by swerve » Fri Feb 09, 2018 6:41 am
Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?

A. 3 hours and 20 minutes.
B. 4 hours and 12 minutes.
C. 4 hours and 48 minutes.
D. 5 hours.
E. 5 hours and 20 minutes.

The OA is C.

Moe's speed = s

Ali's speed = 5s

Then, if both working together, the combined speed will be, 6s, right?

Now, at a rate of 6s, they complete the job in 4 hours. I know that the total work will be, work = speed * time = 6s * 4 = 24s.

Then I need to determine the time that will take Ali to complete the job working alone, at the same rate.

Time = work / speed = 24s / 5s =24/5 hours or 4 hours and 48 minutes.

Please, can any expert explain this PS question for me? I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.
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by ErikaPrepScholar » Fri Feb 09, 2018 7:23 am
You can also approach this problem using the combined work equation: $$\frac{1}{A}+\frac{1}{B}=\frac{1}{A\ and\ B}$$ where the denominators on the left are how long it takes to get the job done alone vs. and the denominator on the right it how long it takes to get the job done together.

If Ali is 5 times faster than Moe, it should takes Moe 5 times as long to complete the job. Let's set the time it takes Ali to complete the job alone to x. This makes the time it takes Moe to complete the job alone 5x. We also know that it takes them 4 hours to complete the job together. Plugging all of this into the combined work equation gives $$\frac{1}{x}+\frac{1}{5x}=\frac{1}{4}$$ We want to solve for how long it would take Ali to complete the job alone, or x:$$\frac{5}{5x}+\frac{1}{5x}=\frac{1}{4}$$ $$\frac{6}{5x}=\frac{1}{4}$$ $$5x=24$$ $$x=\frac{24}{5}$$ $$x=4\frac{4}{5}$$
So it takes Ali 4 and 4/5 hours to complete the job. 4/5 of 60 minutes is 48 minutes, so it takes him 4 hours and 48 minutes.
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by GMATGuruNY » Fri Feb 09, 2018 7:55 am
swerve wrote:Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?

A. 3 hours and 20 minutes.
B. 4 hours and 12 minutes.
C. 4 hours and 48 minutes.
D. 5 hours.
E. 5 hours and 20 minutes
Since Ali's rate is 5 time's Moe's rate, let Moe's rate = 1 unit per hour and Ali's rate = 5 units per hour, for a combined rate of 6 units per hour.
Working together at a rate of 6 units per hour, they complete the job in 4 hours, implying that the job = rt = 6*4 = 24 units.
Since Ali's rate is 5 units per hour, Ali's time to complete the 24-unit job = w/r = 24/5 hours = 4 hours and 48 minutes.

The correct answer is C.
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by Jeff@TargetTestPrep » Mon Feb 12, 2018 4:44 pm
swerve wrote:Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?

A. 3 hours and 20 minutes.
B. 4 hours and 12 minutes.
C. 4 hours and 48 minutes.
D. 5 hours.
E. 5 hours and 20 minutes.
We can let the time it takes Ali to complete the job alone = x hours. His rate is thus 1/x. Since Ali is 5 times faster than Moe, i.e., Moe is â…• as fast as Ali, Moe's rate is (â…•)(1/x) = 1/5x. Since they work together for 4 hours to complete the job, we have:

4(1/x) + 4(1/5x) = 1

Multiplying the entire equation by 5x, we have:

20 + 4 = 5x

24 = 5x

24/5 = x

Thus, it takes Ali 24/5 hours, or 4 4/5 hours, to complete the job by himself. Since 4/5 hour = 4/5 x 60 = 48 minutes, it takes Ali 4 hours and 48 minutes to complete the job.

Answer: C

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