speed/distance

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nehakhas1: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Wed Oct 15, 2008 11:25 amFollowed by: 1 member

by nehakhas1 » Sun Jul 05, 2009 3:32 pm

Mary passed a certain gas station on a highway while traveling west at a constant
speed of 50 miles per hour. Then, 15 minutes later, Paul passed the same gas station
while traveling west at a constant speed of 60 miles per hour. If both drivers
maintained their speeds and both remained on the highway for at least 2 hours, how
long after he passed the gas station did Paul catch up with Mary?
A. 30 min
B. 45 min
C. 1 hr
D. 1 hr 15 min
E. 1 hr 30 min

Ans e

Can you please suggest the shortest way to this ?

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Source: Beat The GMAT — Problem Solving | Sun Jul 05, 2009 3:32 pm

ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

Re: speed/distance

by ssmiles08 » Sun Jul 05, 2009 3:47 pm

nehakhas1 wrote:Mary passed a certain gas station on a highway while traveling west at a constant
speed of 50 miles per hour. Then, 15 minutes later, Paul passed the same gas station
while traveling west at a constant speed of 60 miles per hour. If both drivers
maintained their speeds and both remained on the highway for at least 2 hours, how
long after he passed the gas station did Paul catch up with Mary?
A. 30 min
B. 45 min
C. 1 hr
D. 1 hr 15 min
E. 1 hr 30 min

Ans e

Can you please suggest the shortest way to this ?

I dunno why but I am getting D as my answer.

R of mary = 50
T = t + 1/4 since mary was already 15 minutes on the road when Paul passed the gas station.

R of paul = 60
T = t

50*(t+1/4) = 60*t

50t + 50/4 = 60t

t = 1.25

convert that into minutes = 75 minutes which is 1 hr and 15 minutes.

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v: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Thu Jul 17, 2008 9:04 am; Location: Bangalore

Re: speed/distance

by v » Sun Jul 05, 2009 3:59 pm

Yes u r write,
P will catch M = 75 min
But M time = 90 min.

Any way shortest way is:
Difference in Speed=10
Distance (When P started)=12.5
So Time=12.5/10=1.25 hrs = 75 min.

Vikas Panwar

ssmiles08 wrote:
nehakhas1 wrote:Mary passed a certain gas station on a highway while traveling west at a constant
speed of 50 miles per hour. Then, 15 minutes later, Paul passed the same gas station
while traveling west at a constant speed of 60 miles per hour. If both drivers
maintained their speeds and both remained on the highway for at least 2 hours, how
long after he passed the gas station did Paul catch up with Mary?
A. 30 min
B. 45 min
C. 1 hr
D. 1 hr 15 min
E. 1 hr 30 min

Ans e

Can you please suggest the shortest way to this ?
I dunno why but I am getting D as my answer.

R of mary = 50
T = t + 1/4 since mary was already 15 minutes on the road when Paul passed the gas station.

R of paul = 60
T = t

50*(t+1/4) = 60*t

50t + 50/4 = 60t

t = 1.25

convert that into minutes = 75 minutes which is 1 hr and 15 minutes.

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hwiya320: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Tue Sep 02, 2008 5:34 pm; Thanked: 7 times

by hwiya320 » Sun Jul 05, 2009 4:04 pm

1:15 is incorrect.

The question is how long it would take for you to catch up with Mary after you pass the gas station. Since it took 15 minutes to catch up at 60mph, that means he has traveled 15 miles.

Mary x time + 15 miles = Paul x time

50t+15 = 60t
which equals
15 = 10t
t=3/2 hours or 1.5 hours.

Time to beat the GMAT again.

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dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Sun Jul 05, 2009 5:05 pm

hwiya320 wrote:1:15 is incorrect.

The question is how long it would take for you to catch up with Mary after you pass the gas station. Since it took 15 minutes to catch up at 60mph, that means he has traveled 15 miles.

Mary x time + 15 miles = Paul x time

50t+15 = 60t
which equals
15 = 10t
t=3/2 hours or 1.5 hours.

Mary traveled the 15 minutes at 50 mph before paul reached the gas station. So she traveled 12.5 miles. (you used 60 mph instead of 50 for the distance mary traveled before paul reached the gas station).

Therefore it is

50t + 12.5 = 60t
12.5 = 10t
t = 1.25

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ghacker: Master | Next Rank: 500 Posts; Posts: 148; Joined: Wed Jun 03, 2009 8:04 pmFollowed by: 1 member; Thanked: 18 times

by ghacker » Sun Jul 05, 2009 11:17 pm

refer to the speed(velocity) time graph

Area will give the displacement or the distance covered

Take the gas station as zero / or base point , when Paul catches Mary

The distance Paul traveled from the gas station = the distance Mary traveled from the gas station

From the figure

Dis_t Mary = A+B , Dis_t Paul = B+c , since B is common

We known That when Paul catches Mary Dis_t Paul = Dis_t Mary

So A = C , From geometry A = 50*0.25(50*1/4) , C = 10*(t-1/4)

Then 50*1/4 = 10(t-1/4)

12.5 = 10(t-1/4) ----------> 1.25 = t-1/4

Hence Answer is 1 hour and 15 min

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