Two trains A and B of length 30m and 42 m

Here we will learn about the concept of two trains passes in the same direction.

When two train passes a moving object (having some length) in the same direction.

Let length of faster train be l meters and length of slower train be m meters

Speed of faster train be x km/hr and speed of slower train be y km/hr

Relative speed = (x – y) km/hr

Then, time taken by the faster train to pass the slower train = (l + m) meters/(x – y) km/hr

Note: Change km/hr to m/sec

Now we will learn to calculate when two trains running on parallel tracks (having some length) in the same direction.

Solved examples when two trains passes (having some length) in the same direction:

1. Two trains 130 m and 140 m long are running on parallel tracks in the same direction with a speed of 68 km/hr and 50 km/hr. How long will it take to clear off each other from the moment they meet?

Solution:

Relative speed of trains = (68 – 50) km/hr

= 18 km/hr

= 18 × 5/18 m/sec

= 5 m/sec

Time taken by the train to clear off each other = sum of length of trains/relative speed of trains

= (130 + 140)/5 sec

= 270/5 sec

= 54 sec

2. The two trains are running on parallel tracks in the same direction at 70 km/hr and 50 km/hr respectively. The faster train passes a man 27 second faster than the slower train. Find the length of the faster train.

Solution:

Relative speed of the trains = (70 – 50) km/hr

= 20 km/hr

= 20 × 5/18 m/sec

= 50/9 m/sec

Length of the faster train = relative speed × time taken by train to pass

= 50/9 × 27 m

` = 150 m

Speed of Train

Relationship between Speed, Distance and Time

Conversion of Units of Speed

Problems on Calculating Speed

Problems on Calculating Distance

Problems on Calculating Time

Two Objects Move in Same Direction

Two Objects Move in Opposite Direction

Train Passes a Moving Object in the Same Direction

Train Passes a Moving Object in the Opposite Direction

Train Passes through a Pole

Train Passes through a Bridge

Two Trains Passes in the Same Direction

Two Trains Passes in the Opposite Direction

8th Grade Math Practice

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Text Solution

Solution : Step I: For train `A, u =54" km h"^(-1) =54xx(5)/(18)" ms"^(-1) =15" ms"^(-1)` For t=25s, a=0 using `s=ut +(1)/(2) at^(2)`, we get `s_(1) =15xx25+0=375 m` Thus, the distance traveled by trains A in 25s is 375m. Step II: For train `B, u =54" km h"^(-1) =15" ms"^(-1)` For t =25 s, using `s=ut +(1)/(2) at^(2)," we get "s_(2) =15xx25+(1)/(2) xx2xx2(25)^(2)=275+625=1000 m`. Step III: Let `s_(o)` be the original separation between two trains. Then the distance traveled by train B in 25 sec, so that it just crosses the head of train A, is given by `s_(2) =s_(o) +s_(1)` + length of train A + length of train B. or `1000 = s_(0) + 375 + 300 + 300` ? `s_(0) = 25 m`

Given

Lengths of two trains = 120 m and 80m

The trains are running in opposite directions with velocities 42km hr and 30km hr respectively.

Find out

We have to determine in what time will they completely pass each other

Solution

The relative velocity of one train with respect to second train is,

= 42 – (-30)

= 72 km/hr = 20 m/s

Total distance of two trains to be travelled = 120 + 80

= 200 m

Time taken = Distance / velocity