Let's start with the fundamentals: **Distance = Speed x Time **

Units: **miles = miles per hour x hours **

I will define the variables as follows:

*Speed of Train A* = y

*Speed of Train B *= y + 15 (since it states that "Train B travels 15 mph faster than train A")

*Time* = t = 3 (the time in hours)

Approach to setting up the equation if that the distance traveled by Train B + distance traveled by Train A = total distance

[(y+15) × 3] + [(y) x 3] = 345 - First you can distribute the items in the brackets by multiplying each item by 3

3y + 45 + 3y = 345 - Then you can combine both of the y terms

6y + 45 = 345 - Then subtract 45 from both sides of the equation

- 45 -45 - *Here I'm just showing the subtraction of 45 from each side *

6y = 300 - Finally you can divide both sides of the equation by 6

y = 50 - Now you have arrived at the speed of Train A (50 miles per hour!)

Speed of Train A = y = **50 miles per hour **

Speed of Train B = y + 15 = **65 miles per hour**

Let's double check this...Does distance traveled by Train B + distance traveled by Train A = total distance?

Train A = (50 miles per hour) x (3 hours) = 150 miles traveled in a direction

Train B = (65 miles per hour) x (3 hours) = 195 miles traveled in the opposite direction

Yes! 150 miles + 195 miles = 345 miles total

Ryan M.

10/06/15