BTGModeratorVI wrote: ↑Tue Jul 07, 2020 6:22 am
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
Brent Hanneson - Creator of GMATPrepNow.com
