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Mary passed a certain gas station on a highway while traveli [#permalink]

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01 Nov 2007, 10:28

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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

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

Please confirm if I'm correct

i get D

d = rt

M: r = 50mph, t = t + 1/4hr
d = 50 (t + 1/4)

P: r = 60, t = t
d = 60t

since they went the same distance:
50t + 50/4 = 60t
10t = 50/4
t = 1.25 or 1 hr, 15min

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

First you must realize that Mary went 50mph for 15minutes after she passed the gas station. @ exactly 15min Paul passes the gas station.

15min = 1/4hr So mary went 50/4 miles.

To find out how long it will take Paul to reach Mary, just make Mary's speed 0 and Paul's speed 10.

So t=50/4/10 ---> t=1.25 or 1 1/4 hrs which is 1 hr 15min

Problems like these are best solved using relative speeds. (as done in the above solution).

Paul's speed relative to Mary = 60 - 50 = 10mph Distance to cover = 15 mins x 50 mph = 25/2 miles

Time = (25/2) / 10 = 25/20 = 5/4 = 1hr 15 mins.

Ans D.

Nice explanation. But what if in the same question we have to calculate distance between the gas stattion and meeting point? and what is the purpose of sayin they travelled for at least 2 hrs?
_________________

Problems like these are best solved using relative speeds. (as done in the above solution).

Paul's speed relative to Mary = 60 - 50 = 10mph Distance to cover = 15 mins x 50 mph = 25/2 miles

Time = (25/2) / 10 = 25/20 = 5/4 = 1hr 15 mins.

Ans D.

Nice explanation. But what if in the same question we have to calculate distance between the gas stattion and meeting point? and what is the purpose of sayin they travelled for at least 2 hrs?

Since we know he travelled for 1.25 hours before catching up to her (after passing the gas station), its trivial to calculate the distance between the gas station and their meeting point. 1.25x60 = 75miles

Mary passed a certain gas station on a highway while traveling west at [#permalink]

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01 May 2010, 08:31

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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

Re: Mary passed a certain gas station on a highway while [#permalink]

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23 Feb 2014, 01:55

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Re: Mary passed a certain gas station on a highway while traveli [#permalink]

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05 Oct 2014, 08:08

sidhu4u wrote:

rohityes wrote:

Problems like these are best solved using relative speeds. (as done in the above solution).

Paul's speed relative to Mary = 60 - 50 = 10mph Distance to cover = 15 mins x 50 mph = 25/2 miles

Time = (25/2) / 10 = 25/20 = 5/4 = 1hr 15 mins.

Ans D.

Nice explanation. But what if in the same question we have to calculate distance between the gas stattion and meeting point? and what is the purpose of sayin they travelled for at least 2 hrs?

I also have the same query - what's the purpose of saying both remained on the highway for at least 2 hours?
_________________

Re: Mary passed a certain gas station on a highway while traveli [#permalink]

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05 Oct 2014, 20:05

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windofchange wrote:

sidhu4u wrote:

rohityes wrote:

Problems like these are best solved using relative speeds. (as done in the above solution).

Paul's speed relative to Mary = 60 - 50 = 10mph Distance to cover = 15 mins x 50 mph = 25/2 miles

Time = (25/2) / 10 = 25/20 = 5/4 = 1hr 15 mins.

Ans D.

Nice explanation. But what if in the same question we have to calculate distance between the gas stattion and meeting point? and what is the purpose of sayin they travelled for at least 2 hrs?

I also have the same query - what's the purpose of saying both remained on the highway for at least 2 hours?

That's the distraction. "2 Hours" is not required for computation purpose
_________________

Re: Mary passed a certain gas station on a highway while traveli [#permalink]

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28 Oct 2014, 16:16

I am still confused on this. How do we know they caught up after 1 hour?

I tried with the relative speed approach and realized he was gaining on her at 10mph. but after that I don't get the logic/leap saying total time is 1 hr+ 15 mins? how do we know that is when they caught up?

Re: Mary passed a certain gas station on a highway while traveli [#permalink]

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28 Oct 2014, 18:12

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angelfire213 wrote:

I am still confused on this. How do we know they caught up after 1 hour?

I tried with the relative speed approach and realized he was gaining on her at 10mph. but after that I don't get the logic/leap saying total time is 1 hr+ 15 mins? how do we know that is when they caught up?

Refer diagram below:

Attachment:

ma.jpg [ 28.41 KiB | Viewed 23497 times ]

Let the distance between gas station & meeting point = d

Mary travels for 15 Minutes at speed of 50 Miles/hr before Paul crosses the gas station means

Mary has travelled distance of 50/4 = 12.5 when Paul starts from the gas station

Now, Mary is at point P which is 12.5 Miles away from gas station, so now the remaining distance = (d - 12.5) for which Paul will chase

Time required for Paul to reach the catch point = Time required by Mary to reach the catch point

Equation setup will be as follows

\(\frac{d}{60} = \frac{d-12.5}{50}\)

d = 75 (Distance between Gas station & Catch point)

Speed of Paul = 60 Miles/Hr = 1 Miles/ Minute

Time required by Paul = 75 * 1 = 75 Minutes = 1 Hour 15 Minutes

Re: Mary passed a certain gas station on a highway while traveli [#permalink]

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19 Jan 2015, 12:37

Is my calculation correct?

You know she is 15 minutes further at 50 mph. This is 50/60 miles per minute = 5/6. 5/6 * 15 minutes is 75/6 = 12.5 miles. He goes 10 mph faster(60-50) so the time het will pass her is 1 hour and 15 minutes later(12.5/10=1.25hour).

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