Aptitude - Problems on Trains - Discussion

Let's break it down step by step:

Step 1: Calculate the relative speed of the train concerning the first person:
Relative speed = Distance / Time = (Speed of train - Speed of first person) × (3600 s / 1000 m).
Let's denote the speed of the train as x km/h.
Relative speed = (x - 4.5) km/h × (3600 s /1000 m) = (x - 4.5) × 3.6 m/s

Step 2: Calculate the distance covered when overtaking the first person:
Distance = Relative speed × Time = (x - 4.5) × 3.6 m/s × 8.4 s = 30.24(x - 4.5) m.

Step 3: Similarly, calculate the relative speed and distance for the second person:
Relative speed = (x - 5.4) × 3.6 m/s.
Distance = (x - 5.4) × 3.6 m/s × 8.5 s = 30.6(x - 5.4) m.

Step 4: Since the distance covered is the same in both cases (the length of the train), equate the two expressions:
30.24(x - 4.5) = 30.6(x - 5.4).

Step 5: Solve for x:
x ≈ 72 km/h,
Therefore, the speed of the train is approximately 72 km/h.

There is no need of confusion regarding this problem.
in this problem...train and the two persons are moving in the same direction...

Consider the speed of the train be X km/hr.
**(note:the SPEED and LENGTH remains same in both the cases)****
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now let us consider relative speed of the train w.r.to the first person..we get...(X-1.25)
in similar manner,relative speed w.r.to the second train...we get...(X-1.5)
(NOTE:why i'm doing subtraction here ,since they are moving in the same direction)

now we know,distance=speed*time
(x - 1.25) x 8.4 = (x - 1.5) x 8.5
8.4x - 10.5 = 8.5x - 12.75
0.1x = 2.25
x = 22.5
speed of the train=22.5 * (5/18)=81km/hr

Let be considered x is a length, y is a speed, p1 and p2 both represent the person.

Step 1 : p1, p2 speed given for km/hr, Time is given for seconds so km/hr convert to m/s.


P1 => 4.5 * 5/18 = 1.25 m/sec and,

p2 => 5.4 * 5/18 = 1.5 m/sec.

Step 2 : Length or distance (m) = (train speed - person speed) m/sec * time.

x = (y - 1.25) * 8.4,

=> x = 8.4 y - 10.5,

=> 8.4 y - x = 10.5,

x = (y - 1.5) * 8. 5,

=> x = 8.5 y - 12.75,

=> 8. 5 y - x = 12.75.

Step 3:

8.5 y - x = 12.75

8.4 y - x = 10.5
----------------------
0.1 y = 2.25
----------------------

=> y = 22.5 m/sec.


Step 4 : m/sec convert into km/hr (ans is given for km /hr).

y = 22.5 * 5/18

= 4.5 * 18

= 81.0 km/hr.

It is very simple, now there is two person p1 and p2.
So, first we should find the distance for the two people.
P1 = 4.5 * 5/18 * 8.4,
P1 = 10.5 m/s.
P2 = 5.4 * 5/18 * 8.5,
P2 = 12.75 m/s.
Anyways they are in the same direction so;
Distance = (p2 - p2),
= (12.75 - 10.5),
= 2.25 m/s.
Time = 8.5 - 8.4.
Time = 0.1 sec.
Speed= distance/time * 18/5.
= 2.25/0.1 * 18/5,
= 81 km/hr.
Thank you

Both equations is equated because, distance cover by train for both the person is same, ie. Length of the train.

So in solution calculate the distance cover by train (length of the train) for both the person from given data and then equated them. Because distance covered by train (length of the train) is same for both the person.

x is the length of the train; y is the velocity of the train
x/y=t1 ; x/y=t2
x/(y-1.25)=8.4 ; x/(y-1.5)=8.5

[4.5kmph=1.25m/s ;5.4kmph=1.5m/s]

x-8.4y=-10.75..........(1)
x-8.5y=-12.75..........(2)
solving the equ 1 & 2

we get thge solution y=22.5m/s
there for ans;
the speed of the train y=22.5m/s=81kmph

Let,
Speed of train - x
Train Passes 1st person walking in the same direction
=>Speed = (X-4.5)*8.4.

Train Passes 2nd person walking in the same direction
=> Speed= (X-5.4)*8.5.

Now,
(X-4.5)* 8.4= (X-5.4)* 8.5,
8.4X - 37.8 = 8.5X - 45.9,
45.9 -37.8 = 8.5X - 8.4X,
8.1 = 0.1X,
=>X = 8.1/0.1.
=> X = 81 Km/hr.

Distance means it,s length of train ---------->(x-1.25)*8.4
(x-1.25)------>is relative speed,
8.4----------->time.

Same as in case of (x-1.5)x8.5.

In both cases gives distence of cover it,s idirectly both are same.

So (x-1.25)x8.4=(x-1.5)x8.5-----> find x from this you can get speed

Just covert seconds to hour by dividing 60x60 = 3600.

No more conversions:

Let length be x.
and Speed be y.

8.4/3600 = x/(y-4.5).
8.4y -37.80 = 3600x ...(eq 1).

8.5/3600 = x/(y-5.4).
8.5y-45.90 = 3600x....(eq 2).

Solving both equations will give you, y= 81kmph.

Let the speed of train be x m/s, & the distance be y m; here, 4.5km/hr = 1.25m/s and 5.4km/hr=1.5m/s.

Aaccording to question, y/(x-1.25)=8.4, y=8.4x-10.5 ----(i)
Again, y/(x-1.5)=5.4, y=5.4x-8.1 ----(ii)

Solving (i) & (ii), x =22.5 Ans: 22.5 m/s.