Adam and John leave points x and y towards y and x respectively

Question

Adam and John simultaneously leave points x and y towards y and x respectively and travel in the same route. After meeting each other on the way, Adam takes 4 hours to reach his destination, while John takes 9 hours to reach his destination. If the speed of Adam is 48 mph, what is the speed of John?

A. 72 mph
B. 60 mph
C. 32 mph
D. 80 mph
E. 120 mph

A. 72 mph
B. 60 mph
C. 32 mph
D. 80 mph
E. 120 mph

Chethan92 · Accepted Answer

Distance is the same.
Adam takes 4 hrs to reach his destination,y, at 48mph after both meets at a certain point.
And John takes 9hrs to reach his destination,x, at A mph after both meets at a certain point.
So, John takes more time to reach his destination.
So, Speed of John is less than that of Adam. 
Only C option satisfies.

C is the answer.

effatara · Answer

x______________m________y

Adam and John start simultaneously from Points 'x' and 'y' respectively and travel towards each other. They meet at Point 'm' and continue till they reach 'y' and 'x' respectively. Since Adam and John start simultaneously they obviously take the same time to reach 'm'. In other words, Adam and John take the same period of time to cover 'xm' and 'ym' respectively. Since the ratio of the speeds of two moving objects is equal to the ratio of the distances they travel in any given period of time, we can state that:

Sa/Sj = xm/ym where Sa and Sj are the speeds of Adam and John respectively.
Sa/Sj = 9*Sj/4*Sa (since John and Adam travel 'xm' and 'ym' in 9 and 4 hours respectively)
48/Sj = 9*Sj/4*48
Sj^2 = (4*48^2)/9
 = (96/3)^2
Sj = (96/3) = 32 Ans : C

praveen192 · Answer

The distance will be the same.
Adam will take 4 hours to reach the destination  Y  at 48 mph after both of them meet at a point.
And John will take 9 hours to reach the destination  X  at A mph after both of them meet at a point.
Since John takes more time to reach the destination, his speed is less than that of Adam.

C is the answer.

Ruchirj · Answer

Let's apply a lil bit of logic here....
If adam and John leaves their respective places and meet in between their routes...and after meeting Adam is taking less hour to reach his destination...eventually his speed is more then John and there is only one option left suggesting the correct answer i.e., option c (32)..

Condition-
Even if they are not meeting in the middle of their routes but meet somewhere near to the John's place then it means that Adam travels more distance then John in the same interval of time which is suggesting that Adam's speed is more than John.....

gewinston · Answer

Hello GmatClub,
Could someone work out the number for this anyway? The ratio idea answer was the only post with a numerical answer and a numerical solution would be helpful.

ScottTargetTestPrep · Answer

Solution:
 
We can let n be the number of hours it takes for Adam and John to meet and r be the speed of John. Then the distance between x and y can be expressed as any one of the following:

48(n + 4) (using Adam’s rate and time)

r(n + 9) (using John’s rate and time)

and

(48 + r) * n (using both Adam’s and John’s rates and time when they meet)

Since they represent the same distance, we can set the second and third expressions equal to each other:

r(n + 9) = (48 + r) * n

rn + 9r = 48n + rn

9r = 48n

n = 9r/48 = 3r/16

Now setting the first and second expressions equal to each other and substituting 3r/16 for n, we have:

48(n + 4) = r(n + 9)

48n + 192 = rn + 9r

48(3r/16) + 192 = r(3r/16) + 9r

9r + 192 = 3r^2/16 + 9r

192 * 16 = 3r^2

64 * 16 = r^2

r = 8 x 4 = 32

Alternate Solution:

Notice that if two bodies travel towards each other, the faster body will always reach its destination sooner than the slower body. Since the two bodies will have traveled for an equal time at the moment they meet, the faster body will spend less time after they meet.

Using the above observation, we can determine that Adam travels faster than John since Adam only takes 4 hours to reach point y while John takes 9 hours to reach point x after they meet. The only answer choice less than Adam’s speed of 48 mph is C: 32 mph.

Answer: C

Anu5162 · Answer

Ratio of their speed will be inversely proportional to the square root of time taken after meeting each other
48/S(J) = 3/2 
S(J) = 32

Posted from my mobile device

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Adam and John leave points x and y towards y and x respectively

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