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

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

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New post Updated on: 13 Aug 2018, 06:06
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Question Stats:

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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

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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.
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Re: Two runners, P and Q, competed in a race of 400 m  [#permalink]

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New post 16 May 2018, 18:34
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


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
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Re: Two runners, P and Q, competed in a race of 400 m  [#permalink]

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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
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Re: Two runners, P and Q, competed in a race of 400 m  [#permalink]

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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
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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.
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Re: Two runners, P and Q, competed in a race of 400 m  [#permalink]

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New post 16 Oct 2019, 19:36
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



We see that each stride of P is 2 m long. Therefore, a 400-m race takes him 400/2 = 200 strides. Since he covers 5 strides every 2 seconds, the race takes him 200/5 x 2 = 40 x 2 = 80 seconds.

If we let n = the number of strides of Q per second initially, we can create the equation:

60(4)(n) + 20(4)(n + 1) = 400

240n + 80n + 80 = 400

320n = 320

n = 1

Since the number of strides of Q is 1 per second initially and each stride is 4 m, his speed is 4 x 3600 = 14400 meters per hour, or 14.4 kph.

Answer: E
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Re: Two runners, P and Q, competed in a race of 400 m  [#permalink]

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New post 18 Oct 2019, 02:59
[quote="EgmatQuantExpert"] 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


The time taken by P and Q is same hence 400/5(m/sec) = 80 seconds ~~convert strides to m/sec

initial speed of Q be S and distance covered in 1 min (=60secs) is D gives us D = S*60

400-D = (S +4m/sec) * 20 >>he obviously covers remaining distance in 20 seconds because both finish in total 80 secs.

solving we get 4 mph => 14.4 kph


Took me a while to get it. Although once you know it is not hard!!
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Re: Two runners, P and Q, competed in a race of 400 m  [#permalink]

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New post 19 Oct 2019, 12:54
This is funny. I totally bombed this question but still managed to get the right answer.
I somehow *ASSUMED* that Q started with 1 stride/second. And that translated to 14.4 km/h
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Re: Two runners, P and Q, competed in a race of 400 m   [#permalink] 19 Oct 2019, 12:54
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