Nicky and Cristina are running a 1,000 meter race. Since

ok.. im surprised by the answer...

nicky gets a headstart of 12 seconds.. and in this thime she runs 36 mts (12 * 3)
and by the time christina starts, the gap between them is 36 mts

since christina is faster than nicky by 2 m/s she reduces the gap by 2 m/s

and therefore the whole gap is covered in 18 seconds... but the question is how much time nicky would have run before christina catches up

18 + 12 (the headstart nicky got) = 30

so i think the answer's got to be 30 or the question should be modified to not include the head start time

am i missing something?

Wat's the confusion here?
You are getting the correct ans, same as the OA..
Christina, being faster, runs for 18 secs. Nicki, runs for 30 secs..
ans is 30 secs..

ok.. the OA was changed.... when i first attepmted the problem, the OA was 18 sec

these questions are very easy to answer once they are logically understood.
see Nicky rate of running is 3 meter/sec and he has 12 second head start. so after 12 seconds he has run 36 meters "(3)(12)". now the question tell us that Cristina runs at a pace of 5 meters per second. she is running 2 meter/second faster than nicky (5-3=2). simply divide the 36 meters with 2 you will get the answer. 36/2= 18 seconds.

Here, your answer 18 seconds is the time taken by Cristina.
As Nicky has started 12 seconds early, total time taken by Nicky is 12+18 = 30 Seconds.
So, the answer is D.

Exactly the answer is 30 by adding 18 and 12...i just mentioned that i am placing the logic behind this question to find that 18...thanks by the way...
the other way one can do this question is
Nicky: (RT= D)---- his rate is 3 meter/second and time= t+12sec therefore the distance he covered will be 3(t+12)----------1
Christina: (RT=D)----- her rate is 5 meter/second and time = t therefore the distance she covered will be 5t---------------2

relating two distances
3(t+12) = 5t
t = 18

putting the value of t for nicky t+12 = 18 + 12= 30 and thats the answer

In speed and distance questions drawing a diagram helps in visualizing the problem and easy formulation of the equation.

Given Info
We are given that Nicky runs at a speed of 3 meters/second for 12 seconds before Cristina starts running at a speed of 5 meters/second. We are asked to find the time for which Nicky has run before Cristina catches up with him.

Approach
We know that Distance = Speed * Time. Since we know the speed at which Nicky runs and his head start time we can calculate his head start distance. We also know the speed at which Cristina runs. Once Cristina starts running, they both will run for the same time before Cristina catches up with Nicky.

Since we know the running speeds of both Nicky and Cristina, we can calculate their distance covered in terms of a common variable i.e. the time taken. As Nicky had a headstart, the extra distance covered by Cristina will be equal to the head start distance which Nicky had.

Working Out
Refer the below diagram



Head start time given to Nicky = 12 seconds
Speed at which Nicky runs = 3 meters/second

Distance covered by Nicky = 12 * 3 = 36 meters

Let the time taken by Cristina to catch up with Nicky be t.
Speed at which Cristina runs = 5 meters/second

Distance covered by Cristina in time t = 5t
Distance covered by Nicky in time t = 3t

Since distance covered by Cristina in time t is 36 meters more than that covered by Nicky in time t, we can write

5t = 3t + 36 i.e. t = 18 seconds.

This is the time taken by Cristina to catch up with Nick. Since we are asked to find the time taken by Nicky, we will add the 12 seconds head start he had. So time for which Nicky ran before Cristina caught up with him = 18 + 12 = 30 seconds.

Hope this helps

Regards
Harsh

I guess the total distance is irrelevant here.

Relative Speed is 5 - 3 = 2 mps.

Distance traveled by Cristina in 12 seconds is 36 meters.

So, Nicky will have to catch up 12 * 3 = 36 meters at a speed of 2 mps.

Nicky will catch up in 18 sec.

Christina would have traveled 18 + 12 = 30 seconds.

I guess the total distance is irrelevant here.

Relative Speed is 5 - 3 = 2 mps.

Distance traveled by Cristina in 12 seconds is 36 meters.

So, Nicky will have to catch up 12 * 3 = 36 meters at a speed of 2 mps.

Nicky will catch up in 18 sec.

Christina would have traveled 18 + 12 = 30 seconds.

Let’s let t = the time in seconds that Christina runs until catching up to Nicky. We can create the equation:

3(12 + t) = 5t

36 + 3t = 5t

36 = 2t

18 = t

Including the 12-second head start, Nicky has run 18 + 12 = 30 seconds before Cristina catches up to him.

Answer: D

Cristina

R= 3 meters per second
T-12
D= 3(T-12)

Nicky

R= 5 meters per second
T
D= 5T

5T= 3(T-12)

5T= 3T-36

T=18

Total N running time = 12 + 18 = 30

given that Nicky has lead of 12 sec so distance covered
12*3 ; 36
36+3x= 5x
x = 18
total time of race ; 18+12 ; 30
option D

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