Train A and train B travel towards each other from town A and town B respectively at a constant speed.The two towns are 1320 kilometres apart. After the two trains meet, Train A takes 5 hours to...

Train A and train B travel towards each other from town A and town B respectively at a constant speed.

The two towns are 1320 kilometres apart. After the two trains meet, Train A takes 5 hours to reach town B while Train B takes 7.2 hours to reach town A. How many kilometers does Train A run per hour?

nathanshields | Certified Educator

The trains have run for time t when they meet.   Then the speed of A is given by

`1320/(5+t)=V_a`

and the speed of B is given by

`1320/(7.2+t)=V_b`

We also know that the distances traveled by each train in t hours add to 1320:

`t*Va+t*Vb=1320`

Putting this together we will have an equation in t:

`(1320t)/(5+t)+(1320t)/(7.2+t)=1320`

Divide each term by 1320 (a sloppy way to say "factor 1320 from the left hand side and then divide both sides...):

`t/(5+t)+t/(7.2+t)=1`

Multiply both sides by the denominator of the first fraction:

`t+(t(5+t))/(7.2+t)=5+t`

Multiply both sides by the denominator of the second fraction (the only one left):

t(7.2+t)+t(5+t) = (5+t)(7.2+t)

Now let's multiply this stuff out and try to clean it into a solveable quadratic:

`7.2t+t^2+5t+t^2=36+12.2t+t^2`

`0=36-t^2`