GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Sep 2019, 03:09

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Two runners, P and Q, competed in a race of 400 m

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3024
Two runners, P and Q, competed in a race of 400 m  [#permalink]

### Show Tags

Updated on: 13 Aug 2018, 06:06
13
00:00

Difficulty:

(N/A)

Question Stats:

53% (03:20) correct 47% (03:06) wrong based on 79 sessions

### HideShow timer Statistics

3 common mistakes you must avoid in Distance questions – Practice question 1

Two runners, P and Q, competed in a race of 400 m. P ran at a constant speed of 5 strides in every 2 seconds, covering 10 m in that span. Q started at a constant speed. After running for 1 minute, Q increased its speed by 1 stride per second and finally finished the race at the same time with P. What is Q’s initial speed in kph if Q covered 4 m in every stride?

A. 10 kph
B. 11.5 kph
C. 12.8 kph
D. 13.6 kph
E. 14.4 kph

To solve question 2: Question 2

To read the article: 3 common mistakes you must avoid in Distance questions

_________________

Originally posted by EgmatQuantExpert on 16 May 2018, 07:36.
Last edited by EgmatQuantExpert on 13 Aug 2018, 06:06, edited 6 times in total.
Director
Joined: 31 Jul 2017
Posts: 514
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: Two runners, P and Q, competed in a race of 400 m  [#permalink]

### Show Tags

18 May 2018, 01:53
1
EgmatQuantExpert wrote:
3 common mistakes you must avoid in Distance questions – Practice question 1

Two runners, P and Q, competed in a race of 400 m. P ran at a constant speed of 5 strides in every 2 seconds, covering 10 m in that span. Q started at a constant speed. After running for 1 minute, Q increased its speed by 1 stride per second and finally finished the race at the same time with P. What is Q’s initial speed in kph if Q covered 4 m in every stride?

A. 10 kph
B. 11.5 kph
C. 12.8 kph
D. 13.6 kph
E. 14.4 kph

To solve question 2: Question 2

To read the article: 3 common mistakes you must avoid in Distance questions

Velocity of P = 10/2 = 5m/sec
The total time taken by P = 400/5 = 80 sec.

Now, out of 80 sec, Q has travelled at a constant speed of a fro 60 sec. Therefore, total distance travelled by Q in 60 Sec = 60a. In the remaining 20 sec... for every 1 Sec the velocity of Q increases by 4m/sec.

400 = 60a + 20a + 80
a = 4m/sec = 14.4kmph
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3024
Re: Two runners, P and Q, competed in a race of 400 m  [#permalink]

### Show Tags

Updated on: 20 May 2018, 06:25

Solution

Given:
• Two runners, P and Q, competed in a race of 400 m
• P ran at a constant speed of 5 strides in every 2 seconds, covering 10 m in that span
o Hence, in 2 seconds P covered 10 m
Or, speed of P = $$\frac{10}{2}$$ m/s = 5 m/s
• Q started the race at a constant speed
• Q covered 4 m in every stride
• After running for 1 minute, Q increased its speed by 1 stride per second
• Q finished the race, taking the same time as P

To find:
• The initial speed of Q, in kph

Approach and Working:
• As the race distance is 400 m and speed of P is 5 m/s,
o Time taken by P to finish the race = $$\frac{400}{5}$$ secs = 80 seconds
• Given that the time taken by P and Q is same, Q also takes 80 seconds to finish the race
• Let us assume that in the initial 60 seconds, Q took x strides per second
o Therefore, in the last 20 seconds, Q took (x + 1) strides per second
• As Q covers 4 m in every stride, the total distance covered by Q = 4 [60x +20(x + 1)] m
Or, 4 [60x + 20 (x + 1)] = 400
Or, 60x + 20x + 20 = 100
Or, 80x = 80
Or, x = 1 stride/sec
• Given that Q covered 4 m in every stride, the initial speed of Q = 4 m/s = 4 * $$\frac{18}{5}$$ kph = $$\frac{72}{5}$$ kph = 14.4 kph

Hence, the correct answer is option E.

_________________

Originally posted by EgmatQuantExpert on 16 May 2018, 07:39.
Last edited by EgmatQuantExpert on 20 May 2018, 06:25, edited 1 time in total.
VP
Joined: 07 Dec 2014
Posts: 1233
Re: Two runners, P and Q, competed in a race of 400 m  [#permalink]

### Show Tags

16 May 2018, 18:34
EgmatQuantExpert wrote:
3 common mistakes you must avoid in Distance questions – Practice question 1

Two runners, P and Q, competed in a race of 400 m. P ran at a constant speed of 5 strides in every 2 seconds, covering 10 m in that span. Q started at a constant speed. After running for 1 minute, Q increased its speed by 1 stride per second and finally finished the race at the same time with P. What is Q’s initial speed in kph if Q covered 4 m in every stride?

A. 10 kph
B. 11.5 kph
C. 12.8 kph
D. 13.6 kph
E. 14.4 kph

Q's race, like P's, lasts (400/10)*2=80 seconds
let x=Q's speed in mps in first minute
60*x+20*(x+4)=400
x=4 mps=14.4 kph
E
Non-Human User
Joined: 09 Sep 2013
Posts: 12351
Re: Two runners, P and Q, competed in a race of 400 m  [#permalink]

### Show Tags

11 Aug 2019, 06:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Two runners, P and Q, competed in a race of 400 m   [#permalink] 11 Aug 2019, 06:23
Display posts from previous: Sort by