Question

A train travels due north in a straight line with a constant speed of 100 m/s. Another train leaves a station 2,881 m away traveling on the same track, but traveling due south with a constant speed of 136 m/s. At what position will the trains collide? Round to the nearest whole number.

Answer 1

The trains will collide at a distance 1660 m from the station

Step-by-step explanation:

Let the train traveling due north with a constant speed of 100 m/s be Train A.

Let the train traveling due south with a constant speed of 136 m/s be Train B.

From the question, Train B leaves a station 2,881 m away (that is 2,881 m away from Train A position).

Hence, the two trains would have traveled a total distance of 2,881 m by the time they collide.

∴ If train A has covered a distance
`x` m by the time of collision, then train B would have traveled
`(2881 - x)` m.

Also,

At the position where the trains will collide, the two trains must have traveled for equal time, t.

That is, At the point of collision,

`t_(A) = t_(B)`

`t_(A)` is the time spent by train A

`t_(B)` is the time spent by train B

From,

`Velocity = (Distance )/(Time )\\`

`Time = (Distance)/(Velocity)`

Since the time spent by the two trains is equal,

Then,

`(Distance_(A) )/(Velocity_(A) ) = (Distance_(B) )/(Velocity_(B) )`

`{Distance_(A) = x` m

`{Distance_(B) = 2881 - x` m

`{Velocity_(A) = 100` m/s

`{Velocity_(B) = 136` m/s

Hence,

`(x)/(100) = (2881 - x)/(136)`

`136(x) = 100(2881 - x)\\136x = 288100 - 100x\\136x + 100x = 288100\\236x = 288100\\x = (288100)/(236) \\x = 1220.76m\\`

`x`≅ 1,221 m

This is the distance covered by train A by the time of collision.

Hence, Train B would have covered (2881 - 1221)m = 1660 m

Train B would have covered 1660 m by the time of collision

Since it is train B that leaves a station,

∴ The trains will collide at a distance 1660 m from the station.