equation that relates to speed. equation that relates to distance

Question

2 trains leave Cleveland at the same time. One train travels east and the other travels west. The speed of the westbound train is 4 mph greater than the speed of the eastbound train. After 3 hours, they are 660 miles apart. Find the rate of each train. Assume that the trains travel in a straight line in directly opposite directions.

Answer 1

d=rt

660=e*3+(e+4)*3

660=3e+3e+12

660=6e+12

660-12=6e

648=6e

e=648/6

e=108 mph

e+4=112 mph

Answer 2

Let's say Westbound's speed is W, and Eastbound's speed is E

 

After 3 hours Westbound is at 3W miles of distance from the original point == 3W

 

After 3 hours Easttbound is at 3E miles of distance from the original point == 3E

 

Because they have opposite directions:

 

3E +3W = 660

 

However, W = E + 4  (The speed of the westbound train is 4 mph greater than the speed of the eastbound train)

 

replacing W in the first equation:

 

3E + 3(E + 4) = 660

 

3E + 3E + 12 = 660

 

6E = 648

 

E = 108 mph   =>  W = E + 4  =>  W= 112 mph