A northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The northbound train travels 12 miles per hour faster than the southbound train. After 2.5 hours, they are 330 miles apart

Hello Treena!

This an application of algebra to what is commonly considered a Physics problem.

We must assume the trains start at the same place in their N and S travels. (They left that condition out of the question !)

Vn is the velocity to the North Vs is the velocity to the South.

(Note that these are indeed velocities becasuse they have magnitude and direction!)

Vn is 12 mph bigger than Vs. That means that Vn = Vs +12.

After 2.5 hours the separation of the trains is 300 miles, or algebraically:

( Vs + Vn) mph * 2.5 hrs = 330 miles

Substitue for Vn: ( Vs + Vs +12 ) * 2.5 = 330

Solve for Vs: 2Vs +12 = 330 /2.5

2Vs = (330 / 2.5 ) - 12

Vs = 1/2 *{ (330/2.5) -12 }

Vs = 1/2 * { 132 - 12 }

Vs = 1/2 * { 120 }

**Vs = 60 mph**

Now calculate Vn: Vn =Vs +12

Vn = 60 + 12

**Vn = 72 mph**

Check:** **

** ** South train: Vs mph * 2.5 hrs = 60 * 2.5 = 150 miles

North train: Vn mph * 2.5 hrs = 72 * 2.5 = + 180 miles

Separation after 2.5 hours: 330 miles OK!

Good Luck .... make sure you get on the right train! :-)

*Bruce S*