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# A straight highway connects two cities P and Q, and goes via two check

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Joined: 04 Jan 2015
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A straight highway connects two cities P and Q, and goes via two check  [#permalink]

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Updated on: 13 Aug 2018, 06:12
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Difficulty:

65% (hard)

Question Stats:

56% (01:45) correct 44% (01:57) wrong based on 70 sessions

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Application of Average Speed in Distance problems - Exercise Question #1

A straight highway connects two cities P and Q, and goes via two checkpoints M and N, in that order. A bus started from P and moved to M at an average speed of 30 mph. After crossing M, it increased its speed to 50 mph and moved towards N. When it reached N, it further increased its speed to 60 mph and continued to move at this speed till it reached Q. What is the average speed of the bus throughout the whole journey?

Statement 1: The ratio of time the bus took to cover the distances PM, MN, and NQ respectively is 2:1:3
Statement 2: Out of the three distances, NQ is 3 times the distance PM and more than 3 times the distance MN

Option choices:
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

To solve question 2: Question 2

To read the article: Application of Average Speed in Distance problems

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Originally posted by EgmatQuantExpert on 09 May 2018, 08:31.
Last edited by EgmatQuantExpert on 13 Aug 2018, 06:12, edited 5 times in total.
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Re: A straight highway connects two cities P and Q, and goes via two check  [#permalink]

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09 May 2018, 08:32

Solution

Given:
• A straight highway connects two cities P and Q, and goes via two checkpoints M and N, in that order
• A bus started from P and moved to M at an average speed of 30 mph
• After crossing M, it increased its speed to 50 mph, towards N
• From N, it further increased its speed to 60 mph till it reached Q

To find:
• The average speed of the bus throughout the whole journey

Approach and Working:
The given scenario can be depicted using the following table:

Let us assume that the distance between P and M is x, between M and N is y, and between N and Q is z.
Therefore, the average speed of the whole journey = (x + y + z) / (x/30 + y/50 + z/60)

Analysing Statement 1
• As per the information given in Statement 1, the ratio of time the bus took to cover the distances PM, MN, and NQ respectively is 2:1:3
o Let us assume the time taken for the individual parts of the journey to be 2t, t, and 3t
• As we know the distances are x, y, and z respectively, we can say:
o $$\frac{x}{30}$$ = 2t or, x = 60t
o $$\frac{y}{50}$$ = t or, y = 50t
o $$\frac{z}{60}$$ = 3t or, z = 180t
• We can represent the present scenario as follows:

• Therefore, the average speed = total distance travelled/ total time taken
o Or, average speed = (x + y + z)/(2t + t + 3t) = (60t + 50t + 180t)/6t = $$\frac{290t}{6t} = \frac{145}{3}$$ mph
• Hence, Statement 1 is sufficient to answer

Analysing Statement 2
• As per the information given in Statement 2, out of the three distances, NQ is 3 times the distance PM and more than 3 times the distance MN
o Given that distance NQ is more than 3 times the distance MN, we cannot get any exact value of MN
• Hence, Statement 2 is not sufficient to answer

Hence, the correct answer is Option A.

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Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
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Joined: 28 Jul 2016
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Re: A straight highway connects two cities P and Q, and goes via two check  [#permalink]

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10 Jul 2018, 12:03
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Joined: 02 Sep 2009
Posts: 47967
Re: A straight highway connects two cities P and Q, and goes via two check  [#permalink]

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10 Jul 2018, 14:01
LeonidK wrote:

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Done. Thank you.
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Re: A straight highway connects two cities P and Q, and goes via two check &nbs [#permalink] 10 Jul 2018, 14:01
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