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Mary passed a certain gas station on a highway while traveli

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

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New post 02 Feb 2017, 12:15
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aimeehittinger wrote:
Mary passed a certain gas station on a highway while traveling west at a constant speed of 50 mph. Then, 15 minutes later, Paul passed the same gas station while traveling west at a constant speed of 60 mph. 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


We can classify this problem as a “catch-up” rate problem, for which we use the formula:

distance of Mary = distance of Paul

We are given that Mary passed a certain gas station traveling at a rate of 50 mph and that 15 minutes later Paul passed the same gas station traveling at a rate of 60 mph.

Since Mary passed the gas station 15 minutes before Paul, we can let Paul’s time = t hours and Mary’s time = t + 1/4 hours.

Since distance = rate x time, we can calculate each distance in terms of t.

Mary’s distance = 50(t + 1/4) = 50t + 50/4 = 50t + 25/2

Paul’s distance = 60t

We can equate the two distances and determine t.

50t + 25/2 = 60t

25/2 = 10t

t = (25/2)/10 = 25/20 = 5/4 = 1¼ hours = 1 hour and 15 minutes

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

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New post 11 Feb 2017, 02:19
we can solve the above problem in just 15sec. if we look more closely to the problem as we can see that when they both meet they both have traveled the same distance so we do not need to calculate the distance , we know that when distance is constant then the speed is inversely proportional to the time, so form it we can calculate the speed is multiplied by 5/6 so no the time will multiplied by 6/5 and the difference between time between them equal to 15
such as : 6/5t-t=15
t=75 mins that equal to 1 hr.15 mins
hence the answer is D
thanks
if you liked my post please kudos :)

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

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New post 19 Mar 2017, 20:45
For me, there are two approaches to use.

1) Setting the time that Mary travels as t means that Paul travels for t-15 mins.
D=S*T and we want to find out when the distances from the station to the catch-up point are equal for both Mary and Paul.
60*(t-15)=50t
60t-900=50t
10t=900
t=90
Paul travels for 15mins less than Mary and so Paul's time is 75mins.

2) Using relative speeds we know that Paul's speed in comparison to Mary's speed is 10mph.
We need to know what distance Paul has to make up. Mary was travelling for 15mins before Paul arrived at the station and therefore traveled 50/4=12.5 miles. So, Paul will catch Mary up when he makes up the 12.5miles travelling at 10mph. T=D/S, 12.5/10=1.25h.

Kudos if you like the explanations. Also, please comment if you have alternative methods!

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

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New post 20 Mar 2017, 01:15
rags 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



after 15 minutes as paul is passing the gas station, Mast will be 50 *15/60 = 12.5 miles away
relative speed since they are moving in same direction will be 60 - 50 =10 mph

time taken to cover 12.5 miles = 12.5/10 = 1.25 hours = 1 hour 15 minute

Option D

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

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New post 11 Aug 2017, 01:28
So the speed of Mary is 50m/h and speed of Paul is 60m/hr . Also Paul travels for 15 minutes more than Mary. So the distance between the distance between the gas station and the meeting point is d and the relative speed is 60-50=10mh/hr
Can someone assist me after these steps. Thank you.

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Mary passed a certain gas station on a highway while traveli   [#permalink] 11 Aug 2017, 01:28

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