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MAry passed a certain gaz station on a highway while

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MAry passed a certain gaz station on a highway while [#permalink] New post 07 Jun 2008, 11:51
MAry passed a certain gaz station on a highway while travelling west at a constant speed of 50 miles per hour. Then, 15 minutes later, Paul passed the same gaz station while travelling 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
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Re: drivers [#permalink] New post 07 Jun 2008, 13:47
--> find the distance that Mary travelled in the 15 mins, d=s.t = 50*.25 = 12.5km

setup this equation

12.5 + 50t = 60t
12.5 = 60t
t = 1.25 (hours) = 1hr 15min

d
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Re: drivers [#permalink] New post 08 Jun 2008, 06:39
same answer for me, via same method.
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Re: drivers [#permalink] New post 08 Jun 2008, 11:58
OA is D but could you please explain in more details as I didn't get the calculations.
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Re: drivers [#permalink] New post 08 Jun 2008, 13:12
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puma wrote:
OA is D but could you please explain in more details as I didn't get the calculations.


sure,

basically, the key to this question is realise that the time that Paul passes Mary, the distance from the gas station will be equal for both drivers.

Key equation here is Speed S = distance/time (s=d/t)

so distance = s*t

So lets deal with Mary first. Distance from the gas station upon being passed d = 50t
For Paul, this distance is the same and contains of two portions. Firstly the static distance Paul is behind when he passes the gas station (15 minutes after Mary.). This distance can be computed by 50*0.25 = 12.5km.

The second portion of Pauls distance is 60t. Total distance bein 12.5 + 60t which equals 50t.

therefore t = 1.25 hours = 1hr 15 min
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Re: drivers [#permalink] New post 09 Jun 2008, 12:28
Why when we calculate the first portion of Paul's distance we multiply 50 by 0.25 and not 60?
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Re: drivers [#permalink] New post 09 Jun 2008, 12:44
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I find my way a bit simpler, dunno abt u all

the answer is sure D

15 minutes later when paul reaches the gas stattion , he is 50/4 miles = 12.5 miles behind
now the difference between speed of 2 cars is 60-50 = 10 miles per hour , which means paul will cover 10 miles in 1 hour so he will cover 12.5 miles in 12.5/10 hour .. hence the answer D

I guess all the explanations look at the same thing from different angles ... I tend to avoid a lot of formula based calculations , stick to the fundamental way of thinking like 12.5 miles to cover , its given paul covers 10 miles of the distance between 2 cars in an hour so how much will he take for 12.5 miles ? simple .. down to the basic
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Re: drivers [#permalink] New post 09 Jun 2008, 12:45
maulikmajithia wrote:
I find my way a bit simpler, dunno abt u all

the answer is sure D

15 minutes later when paul reaches the gas stattion , he is 50/4 miles = 12.5 miles behind
now the difference between speed of 2 cars is 60-50 = 10 miles per hour , which means paul will cover 10 miles in 1 hour so he will cover 12.5 miles in 12.5/10 hour .. hence the answer D

I guess all the explanations look at the same thing from different angles ... I tend to avoid a lot of formula based calculations , stick to the fundamental way of thinking like 12.5 miles to cover , its given paul covers 10 miles of the distance between 2 cars in an hour so how much will he take for 12.5 miles ? simple .. down to the basic


excellent method, saved two steps on my method!
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Re: drivers [#permalink] New post 09 Jun 2008, 12:46
you can keep this in mind whenever a person or car or watever has travelled for a duration longer than the other person u must add that to your time
for example in this case paul passes the point 15 minutes after mary hence mary has been travelling for 15 mins longer than paul
also the distances they travel are equal becuase paul is going to catch up with mary

so we can set up the foll equations

Mary
Speed 50
Time t+15/50
Distance d

Paul
Speed 60
Time t
Distance d

Hence we get 50(t+1/4)=d and 60t=d
Simplyfying we get 50t+12.5=60t and eventually t=1.25 which is equivalent to 1 hour and 15 mins

Hope that explains it mate
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Re: drivers [#permalink] New post 10 Jun 2008, 12:52
Thanks to all for the explanation
Re: drivers   [#permalink] 10 Jun 2008, 12:52
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