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?

1 Answer
Aug 10, 2018

Answer:

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]}