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Andy starts his journey from A to B and Ben starts his journey from B

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Andy starts his journey from A to B and Ben starts his journey from B [#permalink]

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New post 21 Dec 2011, 05:50
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Andy starts his journey from A to B and Ben starts his journey from B to A at the same time.After passing each other they complete their journeys in 3 1/3 and 4 4/5 hours respectively.Find the speed of Ben if Andy traveled at 12 miles/hr.


a) 8.33 m/hr
b) 10 m/hr
c) 22 m/hr
d) 20 m/hr
e)16.66 m/hr

[Reveal] Spoiler:
OA is different from what I get.

IMO it should be A. Can someone explain how do u get B as the answer and what is wrong with my approach below ?


My soln goes like this ..
    Person Rate time distance
    Andy 12 m/hr 10/3 40 miles(12*10/3)
    Ben x 24/5 40 miles ( distance has to be the same since its B to A)

hence equating

x*24/5 = 12*10/3
x= 25/3 or 8.33
[Reveal] Spoiler: OA
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Re: Andy starts his journey from A to B and Ben starts his journey from B [#permalink]

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New post 21 Dec 2011, 12:59
rvinodhini wrote:
Andy starts his journey from A to B and Ben starts his journey from B to A at the same time.After passing each other they complete their journeys in 3 1/3 and 4 4/5 hours respectively.


Your calculations look perfect, but I think they answer a different question from the one the question designer intended. I don't find the wording of this question to be good at all, but I'm pretty sure what they mean is this: from the point in time at which Andy and Ben meet, it takes a *further* 3 1/3 hours for Andy to complete his journey, and a *further* 4 4/5 hours for Ben to complete his journey. So if it takes them t hours to meet, Andy will end up traveling for a total of t + 10/3 hours, and Ben a total of t + 24/5 hours. That's a more difficult problem than the one you solved. I don't have time to write up a solution at the moment, but I can later if that would be helpful.
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Re: Andy starts his journey from A to B and Ben starts his journey from B [#permalink]

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New post 22 Dec 2011, 03:02
IanStewart wrote:
rvinodhini wrote:
Andy starts his journey from A to B and Ben starts his journey from B to A at the same time.After passing each other they complete their journeys in 3 1/3 and 4 4/5 hours respectively.


Your calculations look perfect, but I think they answer a different question from the one the question designer intended. I don't find the wording of this question to be good at all, but I'm pretty sure what they mean is this: from the point in time at which Andy and Ben meet, it takes a *further* 3 1/3 hours for Andy to complete his journey, and a *further* 4 4/5 hours for Ben to complete his journey. So if it takes them t hours to meet, Andy will end up traveling for a total of t + 10/3 hours, and Ben a total of t + 24/5 hours. That's a more difficult problem than the one you solved. I don't have time to write up a solution at the moment, but I can later if that would be helpful.


Thanks Stewart .. I tried solving the way you have mentinoed, but ended up with a complex equation (2-3 unknowns) and.Can you please post an easier way of solving this ...
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Re: Andy starts his journey from A to B and Ben starts his journey from B [#permalink]

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New post 22 Dec 2011, 09:51
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rvinodhini wrote:
Andy starts his journey from A to B and Ben starts his journey from B to A at the same time.After passing each other they complete their journeys in 3 1/3 and 4 4/5 hours respectively.Find the speed of Ben if Andy traveled at 12 miles/hr.


a) 8.33 m/hr
b) 10 m/hr
c) 22 m/hr
d) 20 m/hr
e)16.66 m/hr


Suppose Andy and Ben meet at point C. Then we have this diagram:

A---------------C-------------B

Now Andy goes from C to B at 12 mph, and it takes him 10/3 hours, so the distance from C to B is (12)(10/3) = 40 miles. Let's call the distance from A to C 'd'. Then we have:

A--------d-------C-------40------B

Now we know two things. The time it took Andy to travel d miles is the same as the time it takes Ben to travel 40 miles (since they traveled the same amount of time before meeting). If Ben's speed is s, then we know (since time = distance/speed) that

40/s = d/12
480 = sd

Further, we know that it took 24/5 hours for Ben to travel d miles, so

s = d/(24/5)
24s/5 = d

Now substituting this expression for d into the equation above

480 = s * (24s/5)
5*480/24 = s^2
100 = s^2
10 = s

There may well be a faster approach - this is just what I saw to do first.
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Re: Andy starts his journey from A to B and Ben starts his journey from B [#permalink]

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New post 22 Dec 2011, 22:51
IanStewart wrote:
rvinodhini wrote:
Andy starts his journey from A to B and Ben starts his journey from B to A at the same time.After passing each other they complete their journeys in 3 1/3 and 4 4/5 hours respectively.Find the speed of Ben if Andy traveled at 12 miles/hr.


a) 8.33 m/hr
b) 10 m/hr
c) 22 m/hr
d) 20 m/hr
e)16.66 m/hr


Suppose Andy and Ben meet at point C. Then we have this diagram:

A---------------C-------------B

Now Andy goes from C to B at 12 mph, and it takes him 10/3 hours, so the distance from C to B is (12)(10/3) = 40 miles. Let's call the distance from A to C 'd'. Then we have:

A--------d-------C-------40------B

Now we know two things. The time it took Andy to travel d miles is the same as the time it takes Ben to travel 40 miles (since they traveled the same amount of time before meeting). If Ben's speed is s, then we know (since time = distance/speed) that

40/s = d/12
480 = sd

Further, we know that it took 24/5 hours for Ben to travel d miles, so

s = d/(24/5)
24s/5 = d

Now substituting this expression for d into the equation above

480 = s * (24s/5)
5*480/24 = s^2
100 = s^2
10 = s

There may well be a faster approach - this is just what I saw to do first.


I get it now...Thanks for taking time to reply..
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Re: Andy starts his journey from A to B and Ben starts his journey from B [#permalink]

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New post 23 Dec 2011, 01:07
rvinodhini wrote:
Andy starts his journey from A to B and Ben starts his journey from B to A at the same time.After passing each other they complete their journeys in 3 1/3 and 4 4/5 hours respectively.Find the speed of Ben if Andy traveled at 12 miles/hr.


a) 8.33 m/hr
b) 10 m/hr
c) 22 m/hr
d) 20 m/hr
e)16.66 m/hr


When they met they both must have traveled for the same amount of time. Then Andy finished the distance in 10/3 hours while Ben in 24/5 hours. Therefore, it takes Andy less time to travel the same distance. So Andy travels faster and consequently Ben slower. Therefore the correct AC is either a or b. So we could choose with 50% probabillity of being correct.

We could choose one of the 2 to backsolve. If it is correct... Perfect! If it isn't we choose the other AC. We backsolve the one with the easiest numbers so we assume that Ben travels with 10 miles/hour.

After they meet:

Andy travels a total of 10/3*12=40 miles, while Ben travels 10*24/5=48. Therefore, the total distance between A and B is 88 miles.

When they met:

Andy must have traveled 88-40 miles=48 miles in 48/12= 4 hours, while Ben must have traveled 88-48=40miles in 40/10=4 hours. Bingo! Since time is the same the correct answer is B.
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Andy starts his journey from A to B and Ben starts his journey from B [#permalink]

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A similar question has been discussed by VeritasPrepKarishma in Link-1 and Link-2.
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Re: Andy starts his journey from A to B and Ben starts his journey from B [#permalink]

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New post 03 Feb 2018, 20:57
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BOOKMARKED
rvinodhini wrote:
Andy starts his journey from A to B and Ben starts his journey from B to A at the same time.After passing each other they complete their journeys in 3 1/3 and 4 4/5 hours respectively.Find the speed of Ben if Andy traveled at 12 miles/hr.


a) 8.33 m/hr
b) 10 m/hr
c) 22 m/hr
d) 20 m/hr
e)16.66 m/hr

[Reveal] Spoiler:
OA is different from what I get.

IMO it should be A. Can someone explain how do u get B as the answer and what is wrong with my approach below ?


My soln goes like this ..
    Person Rate time distance
    Andy 12 m/hr 10/3 40 miles(12*10/3)
    Ben x 24/5 40 miles ( distance has to be the same since its B to A)

hence equating

x*24/5 = 12*10/3
x= 25/3 or 8.33


We do have a formula for this
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.

\(\frac{12}{Sb} = \sqrt{\frac{(24/5)}{(10/3)}}\)

Sb = 10

And here is a discussion on how to do it without using the formula (also why the formula is what it is)
http://www.veritasprep.com/blog/2013/04 ... -formulas/
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Re: Andy starts his journey from A to B and Ben starts his journey from B   [#permalink] 03 Feb 2018, 20:57
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