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

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On a road trip, Kip drove one-quarter the distance [#permalink] New post 03 Jun 2018, 07:20
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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
[Reveal] Spoiler: OA

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Re: On a road trip, Kip drove one-quarter the distance [#permalink] New post 04 Jun 2018, 02:13
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There are 4 sections in this journey. Each 1/4 of Total.

Lets say total distance is x then, each distance would be \(\frac{1}{4}\) \(*x\)

Speed for each of these four sectors from the 1st to 4th is as follows:

v miles per hour, 2v miles an hour, 4v miles an hour and 8v miles an hour.

To find the total time traveled we have to find the time spent on each of the 4 sectors and add them up.

Total time = \(\frac{1}{4v} * x + \frac{1}{8v} * x + \frac{1}{16v} * x + \frac{1}{32v} * x = \frac{15x}{32v}\)

Therefore average speed = \(\frac{Distance traveled}{time taken}\) = \(\frac{x}{15x}\) divided by 32v = \(\frac{32v}{15}\)
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Re: On a road trip, Kip drove one-quarter the distance [#permalink] New post 04 Jun 2018, 06:22
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GreenlightTestPrep 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


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
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Re: On a road trip, Kip drove one-quarter the distance [#permalink] New post 01 Aug 2019, 14:54
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Here's how I did it.
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Re: On a road trip, Kip drove one-quarter the distance   [#permalink] 01 Aug 2019, 14:54
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On a road trip, Kip drove one-quarter the distance

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