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# Michael left a city in a car traveling directly west. Katie left the

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Math Expert
Joined: 02 Sep 2009
Posts: 59590
Michael left a city in a car traveling directly west. Katie left the  [#permalink]

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01 Jul 2016, 04:28
1
10
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:46) correct 34% (02:17) wrong based on 279 sessions

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Michael left a city in a car traveling directly west. Katie left the same city two hours later going directly east traveling at the same rate as Michael. How long after Katie left will they be 350 miles apart?

(1) An hour and a half after Katie left they are 250 miles apart.
(2) Michael's destination is 150 miles farther than Katie's.

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Joined: 20 Feb 2015
Posts: 737
Concentration: Strategy, General Management
Re: Michael left a city in a car traveling directly west. Katie left the  [#permalink]

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01 Jul 2016, 09:06
1) An hour and a half after Katie left they are 250 miles apart.

At this point Michael has already travelled for 2 hours + 3/2 hours = 7/2 hours, which is the relative time.
relative speed = distance /time = 250*2/7 = 500/7 miles per hour
time taken = 350*7/500 therefore sufficient.

(2) Michael's destination is 150 miles farther than Katie's.

let Katie's destination be x miles , Michael's destination = x+150 miles
total = 2x+150 miles: insufficient
therefore A
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Location: India
Re: Michael left a city in a car traveling directly west. Katie left the  [#permalink]

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01 Jul 2016, 09:15
1
Let the speed be 's'
Let the time taken be 't'

Given: st + s(t + 2) = 350
2st + 2s = 350
2s(t + 1) = 350................(1)

St1: An hour and a half after Katie left they are 250 miles apart. --> t = 3/2 + 2 = 7/2 hrs
7s/2 + 3s/2 = 250.
We can find the value of s.
Substitute s in (1). We can find the time taken.
Sufficient

St2: Michael's destination is 150 miles farther than Katie's. --> Clearly insufficient

Intern
Joined: 24 Jan 2016
Posts: 18
Re: Michael left a city in a car traveling directly west. Katie left the  [#permalink]

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08 Nov 2016, 11:02

For A:

1- Michael drove for 2 hrs before Katie moves.
2- After 1.5 hrs ==> Katie drove for 1.5 hrs and Michael drove for another 1.5 hrs ==> a total of 3 hrs
3- Summing up -1- and -2- the total time will be 5 hrs covering a total distance of 250 km . Enough to get the speed, which is equal for both.

With the velocity, we can get the time of a given distance.
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Joined: 23 Oct 2016
Posts: 31
Re: Michael left a city in a car traveling directly west. Katie left the  [#permalink]

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14 Nov 2016, 08:53
statement 2 obviously not sufficient

Statement 1:

for first 2 hours before Katie left, micheal has driven for 2V miles (where v is the speed of either of them). now after the 2 hours, we can sum up their speeds, so V+V=2V, for 1.5 hours, the distance between them would be 2*1.5*V=3V.
So, 3V+2V=250=> v=50. then, for first 2 hours, Micheal covered 100 miles, remaining 250 miles to be covered, so it is sufficient. please correct bunel
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Re: Michael left a city in a car traveling directly west. Katie left the  [#permalink]

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29 Nov 2016, 06:00
Bunuel wrote:
Michael left a city in a car traveling directly west. Katie left the same city two hours later going directly east traveling at the same rate as Michael. How long after Katie left will they be 350 miles apart?

(1) An hour and a half after Katie left they are 250 miles apart.
(2) Michael's destination is 150 miles farther than Katie's.

since they have the same speed in opposite direction

in the first 2 hours he covered 2S where S is their common speed

from 1

250 = 2s+ 3/2*2s = 5s , thus speed is 50m/h and thus in the first 2 hours M covered 100 miles and in the following hour and a half they each travelled 150/2 = 75 at a rate of 50m/h thus and hour later they will each cover 50miles and become 350miles apart.....SUFF

FROM 2

Destination is irrelevant

A
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Re: Michael left a city in a car traveling directly west. Katie left the  [#permalink]

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29 Sep 2018, 17:30
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Michael left a city in a car traveling directly west. Katie left the   [#permalink] 29 Sep 2018, 17:30
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