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

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

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

[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!!

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

Q finished the race the same time as P did.

How long did it take for P to finish the race?

He covers 10 meters in 2 seconds (strides???)

Speed of P = 5 meters per second

Takes P 80 seconds to finish a 400 meter race


Q starts at one speed for 60 seconds. Call it speed R, where R is measure in meters per second

Covers a distance of: (R) (60)

Therefore it must take him 20 more seconds to finish the race of 400 meters so that he is on time.

His “1 more stride” is additional 4 meters per second. His new speed for this last 20 seconds is: (R + 4)


(Distance covered in 60 seconds) + (distance covered in last 20 seconds) = 400 meter length of race

(R) (60) + (R + 4) (20) = 400

Solve for R and you get: R = 4 meters per second = Q’s initial speed

Now we just need to convert to kilometers per hour.


1,000 meters = 1 km

3,600 seconds = 1 hour


(4 * 3,600)
_________ =
(1 * 1,000)

(4 * 36) / (10) = 144/10 =


14.4 kmph

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if P made 10m in 2sec, then we can calculate the rate \(\frac{10m}{2s}=5 \frac{m}{s}\)

then we have to calculate the time that p took to complete the 400 m race
R*t=D
5*t=400
t=80 sec

Q started at \(Q\frac{m}{s}\) for the first 60 seconds, and because we now that Q ended the race at same time as P, we have just 20 sec for the second interval, in which Q increased its rate by 1 stride. Because Q rate is in \(\frac{m}{s}\) we need to convert that 1 stride to \(\frac{m}{s}\). We were told that Q covered 1 m in every stride, so that additional stride add 4m to Q Rate.

using r*t=d
Q *60sec=D1
(Q+4)*20sec=D2

we now that D1+D2=400

so lets find Q, 60Q+20Q+80=400
\(Q=4\frac{m}{s}\)

the question ask about Q in \(\frac{km}{h}\) so wee need to convert \(4 \frac{m}{s}to\frac{km}{h}\)

\(4\frac{m}{s}*\frac{60s}{1min}*\frac{60min}{1h}*\frac{1km}{1000m}\)

\(\frac{4*6*6}{10}=14,4\frac{km}{h}\)