Two trains A and B start simultaneously from stations X and Y towards

Question

Two trains A and B start simultaneously from stations X and Y towards each other respectively. After meeting at a point between X and Y, train A reaches station Y in 9 hours and train B reaches station X in 4 hours from the time they have met each other. If the speed of train A is 36 km/hr, what is the speed of train B?

(A) 16 km/hr
(B) 24 km/hr
(C) 54 km/hr
(D) 81 km/hr
(E) 86 km/hr

(A) 16 km/hr
(B) 24 km/hr
(C) 54 km/hr
(D) 81 km/hr
(E) 86 km/hr

TarunKumar1234 · Accepted Answer

Let's say after time "t" hrs. both trains met.

As, Total distance travel by A = Total distance travel by B
Or, 36*t+36*9 = B*t+ B*4 (since, After meet, B travelled the remaining distance in less hrs. so, B is fast)
Or, (B-36)*t= 4*(81-B), So 36<B<81

So, I think C.

atharva2005 · Answer

Let the speed of train A and train B be v1 and v2, respectively and the time taken by them after crossing each other be t1 and t2, respectively.

Now, according to formula,

v1/v2 = √(t2/t1)
or, 36/v2= √(4/9)  
or, 36/v2= 2/3
or, v2= (36*3)/2
 = 54 km/hr

Therefore, speed of train B= 54 km/hr.
So, the answer is (C)

(PS: I am in grade 10)

ShankSouljaBoi · Answer

Sqrt ( 9/4 ) = B / A . A = 36 . B comes out to 54 KMPH. C it is

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jrk23 · Answer

Anyone please explain the method for this.

Fdambro294 · Answer

X——————M——————Y

Let speed of A = A
Let speed of B = B

Let M = the meet point that takes them Time T to travel to

(1st)
A covers the distance from XM at the speed of A and takes time T

XM = A * T

B covers the distance from YM at the speed of B and takes time T

YM = B * T

(2nd)
It takes train A 9 hours to cover the rest of the distance after M, which is given by YM

YM = 9 * A

It takes train B 4 hours to cover the rest of the distance after M, which is given by XM

XM = 4 * B

(3rd)
Set up the ratio of distances: XM/YM

XM/YM = (A * T) / (B * T) = A/B

And

XM/YM = (4B) / (9A)

Now set the 2 equations equal

A/B = 4B/9A

Cross multiply

(A)^2 / (B)^2 = 4/9

Now take the square root of both sides

A/B = ratio of speed A - to - speed B = 2/3

Since speed of A = 36

Speed of B = 54

C

This is a special case of 2 trains meeting. The formula is given above. It’s often taught in high schools in foreign counties.

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samarpan.g28 · Answer

I have used the formula v1/v2=√(t2/t1) where v1=36, t1=9, t2=4. So, v2=54 km/hr (C). Please let me know if there are any other methods to solve it.

ROY13 · Answer

Let the point at which the two trains be at Point P which lies between X and Y.
Equating Ratios of time taken,

Time taken by A to cover XP/ Time taken by B to cover XP = Time taken by A to cover PY/Time taken by B to cover PY
=> x/4 = 9/x  (Time taken for both the trains to meet at P will be equal, let that be = x, speed remains uniform for both the trains throughout the journey)
=> x*x = 9*4
=> x = 6

Equating distance;
36*(9+6) = b*(4+6) , b is the speed of the train B
=>b=54

Thanks!

ry0usuke · Answer

can you please explain how this formula is derived?

samarpan.g28 · Answer

I hope this helps you. Give a kudos maybe! :blushing:

Korrigmoi · Answer

What is this formula please I don't understand where it come from ?

Two trains A and B start simultaneously from stations X and Y towards

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