A train passes two persons who are walking in the direction opposite

Question

A train passes two persons who are walking in the direction opposite to which the train is moving, at the rate of 4 m/s and 9 m/s in 8 seconds and 7 seconds respectively. Find the speed of the train ?

(A) 35 m/s
(B) 32 m/s
(C) 31 m/s
(D) 21 m/s
(E) 20 m/s

imeanup · Answer

Let the speed of the Train be  x  m/s.

(4+x)8=(9+x)7

8x-7x=9*7-4*8=63-32=31  m/s

Ans C

SoupBanerjee · Answer

Let speed of the train be  x m/s, and length of the train be  L .

Person 1: 
Moving opposite to the train at 4 m/s; the train passes them in 8s. 
Hence:  L  = 8( 4m/s +  x m/s)

Person 2: 
Moving opposite to the train at 9 m/s; the train passes them in 7s. 
Hence:  L  = 7( 9m/s +  x m/s)

So, 8( 4m/s +  x m/s) = 7( 9m/s +  x m/s). Solving this gives us  x  = 31m/s. Answer option  C .

Formula: Distance=SpeedxTime; and speed is additive for objects moving in opposite direction.

Iotaa · Answer

Person 1 (P1) speed = 4m/s , time to cross= 8 secs
Person 2 (P2) speed = 9m/s , time to cross= 7 secs,

It means in 7 secs train (with the relative speed of person(s) & train) crosses 63 meters & in 8 secs, the train crosses: 32 meters

What does this mean? It means in 1 sec, train must have cross 31 meters (63 meters-32 meters=31 meters).

Hence train speed = Distance / time = 31/1 = 31 m/sec. option C

GmatPoint · Answer

Let the speed of the train be x. Since the train and the persons are walking in opposite directions,
Their relative speed will be (4+x) m/s and (9+x) m/s, respectively.

Also, since speed = distance*time
(4+x)*8 = (9+x)*7
32 + 8x = 63 + 7x
x = 31 m/s

Thus, the correct option is C.

btsaami · Answer

(4+T)8=(9+T)7 where T is the speed of the train.

4+T should be a multiple of 7 for the expression to be equal.
Only option C satisfies the condition. Hence, answer C

soniasw16 · Answer

Why do you equate the 2 together?

KPIB528491 · Answer

The wording makes it sound like two people are moving at 4m/s and 9m/s against the train and we are not given any info about the train. Is this intentional? Very confusingly worded

Krunaal · Answer

The train takes 8 seconds to pass someone moving towards it at 4 m/s, let trains speed be x m/s, so trains length = (x+4)*8

Similarly, it takes 7 seconds to pass someone moving towards it at 9 m/s, so trains length = (x+9)*7

Thus, we equate both as both are nothing but the length of the train.

Yes, two people are moving at 4m/s and 9m/s against the train, and the train passes them.

A train passes two persons who are walking in the direction opposite

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A train passes two persons who are walking in the direction opposite

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