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An athlete runs R miles in H hours...

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An athlete runs R miles in H hours...

by BTGmoderatorLU » Sat Jan 13, 2018 12:49 pm
An athlete runs R miles in H hours, then rides a bike Q miles in the same number of hours. Which of the following represents the average speed, in miles per hour, for these two activities combined?

(A) (R-Q)/H
(B) (R-Q)/2H
(C) [2(R+Q)]/H
(D) [2(R+Q)]/2H
(E) (R+Q)/2H

The OA is E.

I'm confused with this PS question. Experts, any suggestion? I'm not sure about how can I solve. I know that the average speed should be, total distance/total time, right? Thanks in advance.
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by EconomistGMATTutor » Sun Jan 14, 2018 6:42 am
Hello LUANDATO.

Let's take a look at your question.

R miles in H hours implies R/H miles per hour.
Q miles in H hours implies Q/H miles per hour.

Then, the combined average speed is equal to $$\frac{\frac{R}{H}+\frac{Q}{H}}{2}=\frac{R+Q}{2H}.$$

This is why the correct answer is the option E.

I hope this explanation can help you.

Feel free to ask me again if you have a doubt.

Regards.
GMAT Prep From The Economist
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by Jeff@TargetTestPrep » Mon Jan 29, 2018 10:23 am
LUANDATO wrote:An athlete runs R miles in H hours, then rides a bike Q miles in the same number of hours. Which of the following represents the average speed, in miles per hour, for these two activities combined?

(A) (R-Q)/H
(B) (R-Q)/2H
(C) [2(R+Q)]/H
(D) [2(R+Q)]/2H
(E) (R+Q)/2H
We need to determine average speed:

average speed = total distance/total time

average = (R + Q)/(H + H) = (R + Q)/2H

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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by [email protected] » Mon Jan 29, 2018 6:52 pm
Hi LUANDATO,

As far as story problems go, this one is fairly easy from a "logic" standpoint. You can also solve it by TESTing VALUES.

R = 4
H = 2
Q = 6

So the athlete runs 4 miles in 2 hours, then bikes 6 miles in another 2 hours.

Total Distance = 4+6 = 10 miles
Total Time = 2+2 = 4 hours
Average speed = 10/4 = 2.5 miles/hr.

Plugging these values into the answer choices gives us just one match...

Final Answer: E

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