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Charlie drives 30 miles each way to work and back.

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by M7MBA » Fri Apr 13, 2018 6:26 am
Charlie drives 30 miles each way to work and back. If on his drive to work he averages 40 miles per hour, but on his return trip he can only manage an average of 20 miles per hour, what is his average rate for the day, in miles per hour?

(A) 22.5

(B) 26.67

(C) 30

(D) 32.5

(E) 33.33

The OA is B.

I didn't get the correct answer here and I don't know where I made a mistake. Can someone give me some help? Please.
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by Vincen » Fri Apr 13, 2018 7:01 am
Hello M7MBA.

Let's take a look at your question.

- Charlie drives 30 miles each way to work and back.
- On his drive to work, he averages 40 miles per hour. ------ Rate= 30/40 = 3/4 hours.
- On his return trip, he can only manage an average of 20 miles per hour. ------------- Rate = 30/20 = 3/2 hours.

The average speed is Total Distance / Total Time.

Total Distance = 30miles to work + 30 miles to home = 60 miles.
Total Time = 3/4 + 3/2 = 9/4.

Finally, $$Average\ =\ \frac{60}{\frac{9}{4}}=\frac{240}{9}=26.67\ .\ $$ Therefore, the correct answer is the option B.

I hope it helps you.
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by Sionainn@PrincetonReview » Fri Apr 13, 2018 7:48 am
Also if you are tight on time you can quickly narrow down the answers to A and B without doing much math.

The non-weighted average of 20 and 40 is 30. Now we know 30 would be too "easy" for the GMAT and also a bit of a trap since 30 is in the problem. So it likely won't be 30.

It will take Charlie longer to cover the distance when he is traveling at a slower speed. So he will spend more time at the slower speed. This will drag down the non-weighted average of 30, so the true (weighted) average will be less than 30. So we can narrow down the answers to A and B.

Take care,
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by GMATGuruNY » Fri Apr 13, 2018 8:22 am
M7MBA wrote:Charlie drives 30 miles each way to work and back. If on his drive to work he averages 40 miles per hour, but on his return trip he can only manage an average of 20 miles per hour, what is his average rate for the day, in miles per hour?

(A) 22.5

(B) 26.67

(C) 30

(D) 32.5

(E) 33.33
Since the distance in each direction is the same, we can plug in ANY VALUE for the distance.
Let the distance in each direction = the LCM of 40 and 20 = 40 miles.
When Charlie travels the 40-mile distance at 40 mph, the time = d/r = 40/40 = 1 hour.
When Charlie travels the 40-mile distance at 20 mph, the time = d/r = 40/20 = 2 hours.
Average speed for the entire 80-mile trip = (total distance)/(total time) = 80/(1+2) = 80/3 hours.

The correct answer is B.
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by Scott@TargetTestPrep » Thu Jul 05, 2018 3:56 pm
M7MBA wrote:Charlie drives 30 miles each way to work and back. If on his drive to work he averages 40 miles per hour, but on his return trip he can only manage an average of 20 miles per hour, what is his average rate for the day, in miles per hour?

(A) 22.5

(B) 26.67

(C) 30

(D) 32.5

(E) 33.33
We can use the formula for average rate:

average rate = total distance/total time

We know that the total distance is 30 x 2 = 60 miles. Since time = distance/rate, the time to work is 30/40 = 3/4 hour and the time from work is 30/20 = 3/2 hours. Thus,

average rate = (30 + 30)/(3/4 + 3/2)

average rate = 60/(3/4 + 6/4) = 60/(9/4) = 240/9 = 26.67

Answer: B

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