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Speed-Time Problem.

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Speed-Time Problem.

by aman88 » Thu Dec 27, 2012 11:25 am
When a car traveled from Town A to Town B without stopping, the car traveled a total of 2m miles, where m > 0. The car traveled the first m miles at an average speed of v miles per hour, and the car traveled the entire 2m miles at an average speed of miles per hour. What was the average speed of the car, in miles per hour, when it traveled the final m miles?

A. 8v/3
B. 4v
C. 5v
D. 16v/3
E. 8v

OA C
Please let me know how to deal with this problem.

Thanks.
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by GMATGuruNY » Thu Dec 27, 2012 4:34 pm
aman88 wrote:When a car traveled from Town A to Town B without stopping, the car traveled a total of 2m miles, where m > 0. The car traveled the first m miles at an average speed of v miles per hour, and the car traveled the entire 2m miles at an average speed of miles per hour. What was the average speed of the car, in miles per hour, when it traveled the final m miles?

A. 8v/3
B. 4v
C. 5v
D. 16v/3
E. 8v

OA C
The portion in red omits the average speed for the entire 2m miles.
Could you please supply the missing information?
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by aman88 » Thu Dec 27, 2012 11:09 pm
GMATGuruNY wrote:
aman88 wrote:When a car traveled from Town A to Town B without stopping, the car traveled a total of 2m miles, where m > 0. The car traveled the first m miles at an average speed of v miles per hour, and the car traveled the entire 2m miles at an average speed of miles per hour. What was the average speed of the car, in miles per hour, when it traveled the final m miles?

A. 8v/3
B. 4v
C. 5v
D. 16v/3
E. 8v

OA C
The portion in red omits the average speed for the entire 2m miles.
Could you please supply the missing information?
I am sorry. The question reads:

When a car traveled from Town A to Town B without stopping, the car traveled a total of 2m miles, where m > 0. The car traveled the first m miles at an average speed of v miles per hour, and the car traveled the entire 2m miles at an average speed of 5v/3 miles per hour. What was the average speed of the car, in miles per hour, when it traveled the final m miles?
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by Anurag@Gurome » Fri Dec 28, 2012 1:28 am
aman88 wrote:When a car traveled from Town A to Town B without stopping, the car traveled a total of 2m miles, where m > 0. The car traveled the first m miles at an average speed of v miles per hour, and the car traveled the entire 2m miles at an average speed of 5v/3 miles per hour. What was the average speed of the car, in miles per hour, when it traveled the final m miles?
Average speed for 2m miles = 5v/3 miles per hour
Hence, time taken to travel 2m miles = 2m/(5v/3) hours = 6m/5v hours

Average speed for first m miles = v miles per hour
Hence, time taken to travel first m miles = m/v hours

Hence, time taken to travel the final m miles = (6m/5v - m/v) hours = m/5v hours
Hence, average speed for the final m miles = m/(m/5v) mph = 5v miles per hour

The correct answer is C.
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by GMATGuruNY » Fri Dec 28, 2012 6:15 am
aman88 wrote:When a car traveled from Town A to Town B without stopping, the car traveled a total of 2m miles, where m > 0. The car traveled the first m miles at an average speed of v miles per hour, and the car traveled the entire 2m miles at an average speed of 5v/3 miles per hour. What was the average speed of the car, in miles per hour, when it traveled the final m miles?

A. 8v/3
B. 4v
C. 5v
D. 16v/3
E. 8v
Let m=15 and v=3.
Time for the first m miles = d/r = m/v = 15/3 = 5 hours.
Time for the entire 2m miles = d/r = (2m)/(5v/3) = (2*15/( 5*3 / 3 ) = 6 hours.
Since the time for the entire 2m miles is 6 hours, and the time for the first m miles is 5 hours, the time for the last m miles = 6-5 = 1 hour.
Average speed for the last m miles = d/t = 15/1 = 15 miles per hour. This is our target.

Now we plug v=3 into the answers to see which yields our target of 15.
Only C works:
5v = 5*3 = 15.

The correct answer is C.
Last edited by GMATGuruNY on Mon Dec 31, 2012 9:37 am, edited 1 time in total.
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by buzzdeepak » Fri Dec 28, 2012 9:26 am
Another way to explain the answer (personally, this works best for me). Hope this helps.

Set up the problem as R-T-D (Rate - Time - Distance)

R T D
First m miles v t1 m
Next m miles x t2 m
Total 5v/3 T 2m

Since total t = sum of the individual t's, we have:
t1+t2 = T
m/v + m/x = 2m/(5v/3)
Solve for x

I am including an image (apparently all the formatting is getting lost)

Image
[/img]
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