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Math Expert V
Joined: 02 Sep 2009
Posts: 58335
Cyclist M leaves point P at 12 noon and travels at constant velocity  [#permalink]

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1
7 00:00

Difficulty:   35% (medium)

Question Stats: 70% (01:47) correct 30% (01:39) wrong based on 152 sessions

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Cyclist M leaves point P at 12 noon and travels at constant velocity in a straight path. Cyclist N leaves point P at 2 PM, travels the same path at a constant velocity, and overtakes M at 4 PM. What was the average speed of N?

(1) The velocity of Cyclist M was 20 miles per hour.
(2) When Cyclist N overtook Cyclist M, both had traveled 60 miles.

Source: Nova GMAT
Difficulty Level: 600

_________________

Originally posted by Bunuel on 21 May 2017, 11:13.
Last edited by SajjadAhmad on 11 Jul 2019, 05:16, edited 1 time in total.
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1431
Location: India
Re: Cyclist M leaves point P at 12 noon and travels at constant velocity  [#permalink]

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5
When two bodies move in same direction, their relative speed = difference of their speeds
Let velocity of M be m and let velocity of N be n. Their relative speed = n-m
First M moves for 2 hours, let distance covered be D, Then time taken to overtake, t = D/(n-m)

Here N overtakes M in two hours. So D/(n-m) = 2

Statement 1. m=20 mph. So, D = 20*2 = 40 miles So,
40/(n-20) = 2. n = 40 mph. Sufficient

Statement 2. N overtook M at 4 pm and at that time, both had travelled 60 miles.
M covers 60 miles from 12 to 4 pm. So m=60/4 = 15 mph
N covers 60 miles from 2 pm to 4 pm. So n = 60/2 = 30 mph.
Sufficient

(Though I am confused because answers are coming different from the two statements. In GMAT, when the answer is 'D', both statements should give the same answer. Maybe I am missing something)
General Discussion
Director  S
Joined: 21 Mar 2016
Posts: 515
Re: Cyclist M leaves point P at 12 noon and travels at constant velocity  [#permalink]

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Bunuel wrote:
Cyclist M leaves point P at 12 noon and travels at constant velocity in a straight path. Cyclist N leaves point P at 2 PM, travels the same path at a constant velocity, and overtakes M at 4 PM. What was the average speed of N?

(1) The velocity of Cyclist M was 20 miles per hour.
(2) When Cyclist N overtook Cyclist M, both had traveled 60 miles.

it took 2hrs for cyclist N to overtake..

stat1: the relative distance of M and N will be 40 miles.. speed of N is 60,,,suff

stat2: again we can calculate the speed of each,,suff,,

ans D
Intern  S
Joined: 26 Apr 2018
Posts: 38
Re: Cyclist M leaves point P at 12 noon and travels at constant velocity  [#permalink]

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Could someone explain this in as much detail as possible please?
Manager  B
Joined: 30 May 2019
Posts: 63
Location: United States
Concentration: Technology, Strategy
GPA: 3.6
Cyclist M leaves point P at 12 noon and travels at constant velocity  [#permalink]

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Bunuel wrote:
Cyclist M leaves point P at 12 noon and travels at constant velocity in a straight path. Cyclist N leaves point P at 2 PM, travels the same path at a constant velocity, and overtakes M at 4 PM. What was the average speed of N?

(1) The velocity of Cyclist M was 20 miles per hour.
(2) When Cyclist N overtook Cyclist M, both had traveled 60 miles.

Source: Nova GMAT
Difficulty Level: 600

@moderators, Bunuel:
Can someone explain this question to me.
From 1. the avg speed comes to be 20 miles/hr
From 2. the avg speed comes to 30 miles/hr.

Although, the answer comes to D, Isn't the fact that two statements give different answers, not allowed in GMAT questions ? Cyclist M leaves point P at 12 noon and travels at constant velocity   [#permalink] 23 Sep 2019, 21:07
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Cyclist M leaves point P at 12 noon and travels at constant velocity

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