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

## At what speeds are the two trains traveling?he northbound train travels 12 miles per hour faster than the southbound train. After 2.5 hours, they are 330 miles

# 2 Answers

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*

This is a "DiRT" problem, that is a Distance = Rate x Time.

The first step is to identify what the question is asking and label that as your vartiable, like
*x.* In this case it would be the rate (or speed of **both** trains). Since the problem stated that the Northbound train is going faster than the Southbound train, we want to label the Southbound train's rate as
x and the Northbound train 's rate as
x+12.

The second step would be to set up our equation. In this problem, trains are heading in opposite directions. This tells us that the both trains covered is the 330 miles. That means our equation, following the "DiRT" formula, is set up as follows:

Distance (in miles) = Rate (in MPH) * Time (in hours)

330 = (x + [x + 12]) * 2.5

Now all that needs to be done is to solve it. Once you have combine all you can within the parentnsis, you can solve for x by either distrubuting the 2.5 into the binomial or you can divide both sides by 2.5. Whichever way you go, you will find x, the rate of the Southbound train, but then you need to find x + 12 for the rate of the Northbound train.

I hope this helps.