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

It is currently 25 Aug 2019, 15:25

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3018
Two runners, P and Q, competed in a race of 400 m  [#permalink]

Show Tags

New post Updated on: 13 Aug 2018, 06:06
11
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

56% (03:20) correct 44% (03:07) wrong based on 75 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.
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3018
Re: Two runners, P and Q, competed in a race of 400 m  [#permalink]

Show Tags

New post 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.

Answer: 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
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1232
Re: Two runners, P and Q, competed in a race of 400 m  [#permalink]

Show Tags

New post 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
Director
Director
avatar
P
Joined: 31 Jul 2017
Posts: 514
Location: Malaysia
Schools: INSEAD Jan '19
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

New post 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.. !!
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 12096
Re: Two runners, P and Q, competed in a race of 400 m  [#permalink]

Show Tags

New post 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.
_________________
GMAT Club Bot
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

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne