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In the morning, John drove to his mother's house in the

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In the morning, John drove to his mother's house in the  [#permalink]

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New post Updated on: 22 Mar 2013, 13:18
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In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?

(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
(2) John's morning drive lasted 2 hours.

m09 q15

Originally posted by anujtsingh on 22 Mar 2013, 13:01.
Last edited by Bunuel on 22 Mar 2013, 13:18, edited 2 times in total.
Edited the question and moved to DS forum.
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Re: 09 q15[/b] In the morning, John drove to his mother's h  [#permalink]

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New post 22 Mar 2013, 13:17
m09 q15

In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?

The average speed equals to \(\frac{total \ distance}{total \ time}\).

Say the distance between the town and the village is \(d\) kilometers, and the speed from the village to town is \(x\) kilometers per hour, then \(\frac{total \ distance}{total \ time}=\frac{d+d}{\frac{d}{60}+\frac{d}{x}}\) --> \(d\) can be reduced, and we get \(speed=\frac{2}{\frac{1}{60}+\frac{1}{x}}\). So, as you can see we only need to find the average speed from the village to town.

(1) In the evening, John drove at a constant speed of 40 kilometers per hour. Sufficient.

(2) John's morning drive lasted 2 hours. We know nothing about his evening drive. Not sufficient.

Answer: A.

P.S. Please post PS questions in PS forum and DS questions in DS forum. Also do NOT shorten or reword the questions.
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Re: In the morning, John drove to his mother's house in the  [#permalink]

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New post 30 Jul 2013, 17:17
In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?

(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
When getting the average speed of two or more speeds, the distance (think of it like a weighted average) comes into play. In this case, the distance is the same for both speeds as he is traveling a route then traveling in the opposite direction on said route.
SUFFICIENT

(2) John's morning drive lasted 2 hours.
This allows us to get the distance of the route but we don't know how fast he drove on the return home.
INSUFFICIENT

(A)
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Re: In the morning, John drove to his mother's house in the  [#permalink]

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New post 30 Dec 2016, 02:00
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statement 1. as distance is constant then we can apply direct formula 2xy/x+y= average rate here x=60 and y=40 then putting the values in formula we get 2*60*40/60+40= 48km/hr. hence suff.

statement2. no info. about another rate form village to town so insuff.
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Re: In the morning, John drove to his mother's house in the  [#permalink]

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New post 11 Jan 2018, 15:05
anujtsingh wrote:
In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?

(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
(2) John's morning drive lasted 2 hours.


We are given that John drives at a rate of 60 km per hour and drives at a lesser rate when driving again later. We also are given that the distances driven are the same and need to determine the average rate.

We can use the formula:

average speed = total distance/total time

Statement One Alone:

In the evening, John drove at a constant speed of 40 kilometers per hour.

Since the distance each way is d, we can let time 1 = d/60, and time 2 = d/40; thus:

average speed = 2d/(d/60 + d/40)

average speed = 2d/(2d/120 + 3d/120)

average speed = 2d/(5d/120)

average speed = 240d/5d = 48

Statement one alone is sufficient to answer the question.

Statement Two Alone:

John's morning drive lasted 2 hours.

Knowing only the total time is not enough to determine the average speed.

Answer: A
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Re: In the morning, John drove to his mother's house in the   [#permalink] 11 Jan 2018, 15:05
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