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Two cars A and B start from Boston and New York respectively [#permalink]
 28 Apr 2012, 20:50
Question Stats:
44% (04:01) correct
55% (01:47) wrong based on 14 sessions
Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 40 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York? A. 1 hour B. 1 hour 10 minutes C. 2 hours 30 minutes D. 1 hour 40 minutes E. 2 hours 10 minutes
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Re: speed distance time [#permalink]
29 Apr 2012, 01:24
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If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds
\frac{Sa}{Sb} = \sqrt{\frac{Time taken by B}{Time taken by A}}
Hence:
\frac{Sa}{Sb} = \sqrt{\frac{90}{40}}
\frac{Sa}{Sb} = \frac{3}{2}
Hence, time taken by A to cover the same distance which B covers in 90 minutes is:
Ta = \frac{90*2}{3}
Ta = 60 minutes
Hence, total time of A = 40 minutes + 60 minutes = 1 hour 40 minutes
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Re: Two cars A and B start from Boston and New York respectively [#permalink]
29 Apr 2012, 23:25
hi Paragkan,
how did you get to the formula related to ratio of speed at the first place?
thanks,
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Re: Two cars A and B start from Boston and New York respectively [#permalink]
29 Apr 2012, 23:27
I think he is just applying the formulae speed = distance/time . So the train travelling from NY to boston is travelling at a greater speed.
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Re: Two cars A and B start from Boston and New York respectively [#permalink]
29 Apr 2012, 23:31
Hi Vdadwal,
I tried applying speed, time and distance formula too but I could reach the formula paragkan has stated.
thanks,
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Re: Two cars A and B start from Boston and New York respectively [#permalink]
30 Apr 2012, 00:53
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vdadwal wrote: Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 40 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?
A. 1 hour
B. 1 hour 10 minutes
C. 2 hours 30 minutes
D. 1 hour 40 minutes
E. 2 hours 10 minutes Look at the diagram below: Attachment: 
Boston - New York.png [ 4.56 KiB | Viewed 2559 times ]
The rate of car A is a and the rate of B is b; The distance covered by A before the meeting point is x and the istance covered by B before the meeting point is y; Time before meeting t. Since car A covered the distance of y in 40 minutes then the rate of car A = distance/time = a=\frac{y}{40}, but the same distance of y was covered by car B in t minutes, so y=bt --> a=\frac{bt}{40}; Since car B covered the distance of x in 90 minutes then the rate of car B = distance/time = b=\frac{x}{90}, but the same distance of x was covered by car A in t minutes, so x=at --> b=\frac{at}{90}; Substitute b in the first equation: a=\frac{at}{90}*\frac{t}{40} --> reduce by a and cross-multiply: t^2=3600 --> t=60 minutes, hence it took car A 60+40=100 minutes to cover the whole distance. Answer: D. Hope it's clear.
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Re: Two cars A and B start from Boston and New York respectively [#permalink]
30 Apr 2012, 01:28
hi Bunuel, Thanks a lot for the explanation.  Is there any general concept I can follow in these speed, rate, and distance questions. I mean looking at the question I had no fixed approach towards the answer because I saw felt information was too little. It would more helpful if you can share how do YOU approach these type questions. p.s: Kudos +1 thanks,
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Re: Two cars A and B start from Boston and New York respectively [#permalink]
30 Apr 2012, 02:31
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Re: Two cars A and B start from Boston and New York respectively [#permalink]
30 Apr 2012, 03:46
kartik222 wrote: hi Paragkan,
how did you get to the formula related to ratio of speed at the first place?
thanks, I read that formula in some book. I have not derived it
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Re: Two cars A and B start from Boston and New York respectively [#permalink]
30 Apr 2012, 04:05
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Re: speed distance time [#permalink]
30 Dec 2012, 08:16
paragkan wrote: If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds
\frac{Sa}{Sb} = \sqrt{\frac{Time taken by B}{Time taken by A}}
Hence:
\frac{Sa}{Sb} = \sqrt{\frac{90}{40}}
\frac{Sa}{Sb} = \frac{3}{2}
Hence, time taken by A to cover the same distance which B covers in 90 minutes is:
Ta = \frac{90*2}{3}
Ta = 60 minutes
Hence, total time of A = 40 minutes + 60 minutes = 1 hour 40 minutes Great formula. I solved the question the conventional way but took a whopping 4.5 minutes to do so. It took 2 minutes to figure out itself.  The formula will surely help.
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Re: Two cars A and B start from Boston and New York respectively [#permalink]
14 Mar 2013, 03:48
Bunuel wrote: vdadwal wrote: Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 40 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?
A. 1 hour
B. 1 hour 10 minutes
C. 2 hours 30 minutes
D. 1 hour 40 minutes
E. 2 hours 10 minutes Look at the diagram below: Attachment: Boston - New York.png The rate of car A is a and the rate of B is b; The distance covered by A before the meeting point is x and the istance covered by B before the meeting point is y; Time before meeting t. Since car A covered the distance of y in 40 minutes then the rate of car A = distance/time = a=\frac{y}{40}, but the same distance of y was covered by car B in t minutes, so y=bt --> a=\frac{bt}{40}; Since car B covered the distance of x in 90 minutes then the rate of car B = distance/time = b=\frac{x}{90}, but the same distance of x was covered by car A in t minutes, so x=at --> b=\frac{at}{90}; Substitute b in the first equation: a=\frac{at}{90}*\frac{t}{40} --> reduce by a and cross-multiply: t^2=3600 --> t=60 minutes, hence it took car A 60+40=100 minutes to cover the whole distance. Answer: D. Hope it's clear. Bunuel, You are a genius Hats off to you. I can die to have brains like you.
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Re: speed distance time [#permalink]
18 Mar 2013, 02:56
eaakbari wrote: paragkan wrote: If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds
\frac{Sa}{Sb} = \sqrt{\frac{Time taken by B}{Time taken by A}}
Hence:
\frac{Sa}{Sb} = \sqrt{\frac{90}{40}}
\frac{Sa}{Sb} = \frac{3}{2}
Hence, time taken by A to cover the same distance which B covers in 90 minutes is:
Ta = \frac{90*2}{3}
Ta = 60 minutes
Hence, total time of A = 40 minutes + 60 minutes = 1 hour 40 minutes Great formula. I solved the question the conventional way but took a whopping 4.5 minutes to do so. It took 2 minutes to figure out itself. The formula will surely help. There are many formulas that you can learn to cover the various specific question demands but it is not feasible to remember them all. It will be much better if you try to logically figure it out in case you are unable to recall the formula at crunch time. Think of the situation when they meet: (Boston) A->____________________M_________<-B (New York) A starts from Boston and B from New York simultaneously. After some time, say t mins of travel, they meet at M. Since A covers the entire distance of Boston to New York in (t + 40) mins and B covers it in (t + 90) mins, A is certainly faster than B and hence the point M is closer to New York. Distance between Boston and M/Distance between M and New York = Time taken to go from Boston to M/Time taken to go from M to New York = t/40 = 90/t t = 60 mins (distance varies directly with time) So A takes 60 mins + 40 mins = 1 hr 40 mins to cover the entire distance.
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Re: speed distance time
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18 Mar 2013, 02:56
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