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# Dawn chases her young brother Paul. She runs at a constant speed, six

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Dawn chases her young brother Paul. She runs at a constant speed, six  [#permalink]

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30 May 2015, 00:54
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65% (hard)

Question Stats:

61% (01:57) correct 39% (01:54) wrong based on 253 sessions

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Dawn chases her young brother Paul. She runs at a constant speed, six times as fast as 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

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Re: Dawn chases her young brother Paul. She runs at a constant speed, six  [#permalink]

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30 May 2015, 03:05
Simple question...

Acco to me..... First half of the question is not needed to solve the question.

Effectively, the question starts when Dawn overtakes Paul. (lets assume Dawn speed= 6mts/sec; and Paul speed= 1mts/sec)

The relative speed= 5 mts/sec. Running at 5 mts/ sec for 2 mins= 5 X2X60 distance covered. = 600 meters.

Paul running at 1m/sec= covers 10 meters in 10 minutes.

reto wrote:
Dawn chases her young brother Paul. She runs at a constant speed, six times as fast as 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

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Re: Dawn chases her young brother Paul. She runs at a constant speed, six  [#permalink]

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01 Jun 2015, 02:53
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Let pauls speed be x and so, dawns speed is 6x
relative speed between the two = 6x-x=5x
Relative Distance traveled in two mins=5x*2=10x
Time needed to cover that ditance =10x/x=10mins
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Re: Dawn chases her young brother Paul. She runs at a constant speed, six  [#permalink]

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18 Jun 2015, 03:00
reto wrote:
Dawn chases her young brother Paul. She runs at a constant speed, six times as fast as 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

I picked some numbers here:

Speed Dawn= D = 60 miles per minute
Speed Paul = P = 10 miles per minute (D is six times as fast as P)

after 2 minutes D ran a distance of 120 miles.
after 2 minutes P ran a distance of 20 miles

--> D is 100 miles ahead of P

P needs: time = Distance/Rate = 100miles / 10mpm = 10 minutes

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Dawn chases her young brother Paul. She runs at a constant speed, six  [#permalink]

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21 Sep 2016, 19:37
Top Contributor
The relative rate is $$6x-x=5x$$. The relative time is $$x:5x$$ and therefore if $$x=2$$, then $$5x=10$$.
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Re: Dawn chases her young brother Paul. She runs at a constant speed, six  [#permalink]

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22 Sep 2016, 17:32
1
1
Another way to think about it:

The ratio of speeds is 1:6
So ratio of time taken to cover the same distance will be 6:1.
When Dawn overtakes Paul, they are at the same point. When finally Paul catches up to her, they are again at the same point so distance traveled is the same.
If Dawn takes 2 mins to travel that distance, Paul takes 6*2 = 12 mins to travel it.
So After 2 mins, Dawn waits for the next 10 mins while Paul catches up.
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Re: Dawn chases her young brother Paul. She runs at a constant speed, six  [#permalink]

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01 Dec 2016, 03:20
Dawn's Rate=6x
Paul's Rate=x

From start to overtake: D=5xt
After overtake: Dawn goes 6x*2=12x, Paul goes x*2=2x
After stop, the distance between is: (5xt+12x)-(5xt+2x)=10x
Time of stop is: (10x)/x=10min

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Dawn chases her young brother Paul. She runs at a constant speed, six  [#permalink]

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01 Dec 2016, 19:54
Dawn chases her young brother Paul. She runs at a constant speed, six times as fast as 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

let s=Paul's speed in units per minute
in the 2 minutes after overtaking Paul, Dawn runs 2*6s=12s units
in the same 2 minutes, Paul runs 2s units
Paul is now 12s-2s=10s units behind Dawn
10s/s=10 minutes for Dawn to wait for Paul
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Re: Dawn chases her young brother Paul. She runs at a constant speed, six  [#permalink]

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22 Feb 2018, 16:29
reto wrote:
Dawn chases her young brother Paul. She runs at a constant speed, six times as fast as 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

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Re: Dawn chases her young brother Paul. She runs at a constant speed, six &nbs [#permalink] 22 Feb 2018, 16:29
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