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

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pm; Followed by:1 members

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

by BTGModeratorVI » Tue Jul 07, 2020 6:22 am

Timer

00:00

Your Answer

Global Stats

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

Quote

Source: Beat The GMAT — Problem Solving | Tue Jul 07, 2020 6:22 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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

by Brent@GMATPrepNow » Tue Jul 07, 2020 7:43 am

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

Quote

swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

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

by swerve » Thu Jul 09, 2020 11:20 am

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

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 \(12 \cdot 3 = 36\) meters at a speed of 2 mps.

Nicky will catch up in 18 sec.

Christina would have traveled \(18 + 12 = 30\) seconds.

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8084; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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

by Scott@TargetTestPrep » Sat Jul 11, 2020 1:12 pm

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

Solution:

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]