Dawn chases her young brother Paul. She runs at a...

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AAPL: Moderator; Posts: 2685; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Sat Feb 17, 2018 1:02 pm

Dawn chases her younger brother Paul. She runs at a constant speed, six times as fast he does. After Dawn overtakes Paul, she goes on running at the same speed for two more minutes, and then stops and waits for Paul to reach her. If Paul maintains his constant speed throughout the chase, how many minutes does Dawn wait for Paul?

A. 5
B. 6
C. 8
D. 10
E. 12

The OA is D.

Is there a strategic approach to solve this PS question? Can any experts help me, please? Thanks!

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Source: Beat The GMAT — Problem Solving | Sat Feb 17, 2018 1:02 pm

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Sun Feb 18, 2018 4:19 am

Hello AAPL.

Let's take a look at your question.

Let's assume Dawn speed is 6mts/sec and Paul speed= 1mts/sec.

The combined speed is 5 mts/sec.

If she ran for 2 minutes, then their distance is (5mts/sec)*(120sec)=600mts.

Paul running at 1m/sec covers 600 meters in 600 secs = (600sec)*(1minute/60 sec) = 10 minutes.

This is why the correct answer is the option D.

I hope it helps.

Regards.

GMAT Prep From The Economist
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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Thu Feb 22, 2018 4:53 pm

AAPL wrote:Dawn chases her younger brother Paul. She runs at a constant speed, six times as fast he does. After Dawn overtakes Paul, she goes on running at the same speed for two more minutes, and then stops and waits for Paul to reach her. If Paul maintains his constant speed throughout the chase, how many minutes does Dawn wait for Paul?

A. 5
B. 6
C. 8
D. 10
E. 12

We can let Paul's rate = r, so Dawn's rate = 6r.

Let t = the number of minutes Dawn has waited for Paul, we have:

6r(2) = r(2 + t)

12r = 2r + tr

10r = tr

10 = t

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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