Question

Two Train speeds?

Two trains stations, A and B, are 300km apart. Two trains leave A and B simultaneously and proceed at constant speeds to other station. The train from A reaches station B nine hours after trains have met, and the train from B reaches the station A four hours after the trains have met. Find the speed of each train?

Answer 1

One solution is `v_A=20 km h^-1` and `v_B=30kmh^-1`

Explanation:

Let the speeds of the train be `=v_A` and `=v_B`

The time taken by train `A` to reach `B` is

`t_A=300/v_A`

The time taken by train `B` to reach `A` is

`t_B=300/v_B`

Let the meeting point be `x` km from `A`

The time taken by train `A` to reach the meeting point with `B` is

`t_(1A)=x/v_A`

The time taken by train `B` to reach the meeting point with `A` is

`t_(1B)=(300-x)/v_B`

Then

`t_A=t_(1A)+9=x/v_A+9`

and

`t_B=t_(1B)+4=(300-x)/v_B+4`

`300/v_A=x/v_A+9`.......................`(1)`

`300/v_B=(300-x)/v_B+4`..........................`(2)`

Solving equations `(1)` and `(2)`

`300=x+9v_A`

`x=300-9v_A`

`300/v_B=(300-(300-9v_A))/v_B+4`

`300=9v_A+4v_B`

This is a Diophantine equation

One solution is

`v_A=20 km h^-1`

`v_B=30kmh^-1`

graph{(9x+4y-300)=0 [-104.4, 106.45, -27.4, 78.1]}