Problem Solving

AAPL wrote:Manhattan GMAT

Nicky and Cristina are running a 1,000-meter race. Since Cristina is faster than Nicky, she gives him a 12 seconds 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

OA D

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

Hi All,

We're told that Nicky and Cristina are running a 1,000-meter race and since Cristina is faster than Nicky, she gives him a 12 seconds head start. Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second. We're asked how many seconds Nicky will have run before Cristina catches up to him. This is an example of a "chase down" question (in which one entity gets a 'head start' and then a second entity eventually catches-up to the first). These questions can be solved in a couple of ways, including by TESTing THE ANSWERS. Let's start by TESTing Answer B...

Answer B: 18 seconds
IF.... Nicky runs for 18 seconds, then he runs (18)(3) = 54 meters
Since Nicky had a 12 second head start, Cristina runs for just 18 - 12 = 6 seconds
Cristina runs (6)(5) = 30 meters, meaning that she has NOT caught up with Nicky yet. Thus, they both need to run for a LONGER period of time. Let's TEST Answer D next...

Answer D: 30 seconds
IF.... Nicky runs for 30 seconds, then he runs (30)(3) = 90 meters
Since Nicky had a 12 second head start, Cristina runs for 30 - 12 = 18 seconds
Cristina runs (18)(5) = 90 meters. This is the same distance that Nicky runs, so Cristina has caught-up to Nicky and this MUST be the answer.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

AAPL wrote:Manhattan GMAT

Nicky and Cristina are running a 1,000-meter race. Since Cristina is faster than Nicky, she gives him a 12 seconds 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

OA D

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