Two Train speeds?

Question

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?

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Answer 1 · 2018-08-10T09:07:03

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

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]}