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On a road trip, Kip drove one-quarter the distance at an ave

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On a road trip, Kip drove one-quarter the distance at an ave

by Brent@GMATPrepNow » Sun Jun 03, 2018 7:12 am

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On a road trip, Kip drove one-quarter the distance at an average speed of v miles per hour, one-quarter the distance at an average speed of 2v miles per hour, one-quarter the distance at 4v miles per hour, and one-quarter the distance at 8v miles per hour. In terms of v, what was Kip's average speed (in miles per hour) for the entire trip?

A) 15/4v
B) 15v/4
C) 32v/15
D) 4v/15
E) 15v/32

Answer: C
Difficulty level: 600 - 650
Source: www.gmatprepnow.com
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by Brent@GMATPrepNow » Mon Jun 04, 2018 6:18 am
Brent@GMATPrepNow wrote:On a road trip, Kip drove one-quarter the distance at an average speed of v miles per hour, one-quarter the distance at an average speed of 2v miles per hour, one-quarter the distance at 4v miles per hour, and one-quarter the distance at 8v miles per hour. In terms of v, what was Kip's average speed (in miles per hour) for the entire trip?

A) 15/4v
B) 15v/4
C) 32v/15
D) 4v/15
E) 15v/32

Answer: C
Difficulty level: 600 - 650
Source: www.gmatprepnow.com
Since we aren't told the total distance, let's assign a nice value to the distance.
Let's say 32 miles = TOTAL distance.
So, each quarter = 8 miles

Average speed = total distance/total travel time
So, we must find the travel time for EACH QUARTER and add them together.

Time = distance/speed, so:
Time spent driving v mph = 8/v = 8/v
Time spent driving 2v mph = 8/2v = 4/v
Time spent driving 4v mph = 8/4v = 2/v
Time spent driving 8v mph = 8/8v = 1/v

TOTAL travel time = 8/v + 4/v + 2/v + 1/v
= 15/v

Average speed = total distance/total travel time
= 32/(15/v)
= (32)(v/15)
= 32v/15

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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