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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
On a road trip, Kip drove one-quarter the distance
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03 Jun 2018, 07:20
03 Jun 2018, 07:20
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71% (02:25) correct
28% (02:10) wrong based on 83 sessions
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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
A) 15/4v
B) 15v/4
C) 32v/15
D) 4v/15
E) 15v/32
Re: On a road trip, Kip drove one-quarter the distance
[#permalink]
04 Jun 2018, 02:13
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 = \(\frac{32v}{15}\)
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 = \(\frac{32v}{15}\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: On a road trip, Kip drove one-quarter the distance
[#permalink]
04 Jun 2018, 06:22
04 Jun 2018, 06:22
1
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
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
