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

BTGModeratorVI wrote: ↑

Wed Feb 26, 2020 4:24 pm

Nicky and Cristina are running a 1,000 meter race. Since Cristina is faster than Nicky, she gives him a 12 second head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?

(A) 15 seconds
(B) 18 seconds
(C) 25 seconds
(D) 30 seconds
(E) 45 seconds

Answer: D
Source: Manhattan Prep

Since Nicky would have run for 12 seconds before Christina would start, Nicky would have a lead of 3*12 = 36 meters.

So, Christina has to cover 36 meters to pass Nicky.

We know that Christina's speed is 5 meters/sec and Nickey's speed is 3 meters/sec, so Christina's relative speed is 5 – 3 = 2 meters/sec

So, time taken by Christina to cover 36 meters = 36/2 = 18 seconds.

Nicky would have run 12 + 18 = 30 seconds before Cristina catches up to her.

The correct answer: D

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Wed Feb 26, 2020 4:24 pm

Nicky and Cristina are running a 1,000 meter race. Since Cristina is faster than Nicky, she gives him a 12 second head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?

(A) 15 seconds
(B) 18 seconds
(C) 25 seconds
(D) 30 seconds
(E) 45 seconds

Answer: D
Source: Manhattan Prep

GIVEN: Nicki is given a 12-second head start
Nicky runs at a pace of 3 meters per second
distance = (speed)(time)
Plug in values to get: distance = (3 meters per second)(12 seconds) = 36 meters
Nicki's head start = 36 meters

At this point the question becomes a shrinking gap question
(5 meters per second) - (3 meters per second) = 2 meters per second
So the gap shrinks at a rate of 2 meters per second

So we want to find the time it takes the gap to shrink from 36 meters to 0 meters
That is, the gap shrinks a total of 36 meters, at a rate of 2 meters per second

Time = Distance/Speed
Time = 36/2 = 18 seconds

How many seconds will Nicky have run before Cristina catches up to him?
IMPORTANT: Since we want to find Nicky's TOTAL running time, we must also include the 12 seconds he ran during his head start.

TOTAL running time = 18 seconds + 12 seconds = 30 seconds


Answer: D

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Feb 26, 2020 4:24 pm

Nicky and Cristina are running a 1,000 meter race. Since Cristina is faster than Nicky, she gives him a 12 second head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?

(A) 15 seconds
(B) 18 seconds
(C) 25 seconds
(D) 30 seconds
(E) 45 seconds

Answer: D
Source: Manhattan Prep

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