Solving a distance, rate, time problem using a linear equation

Question

Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at 70 miles per hour. The eastbound train travels at 8 miles per hour. How long will it take for the two trains to be 360 miles apart?

Do not do any rounding.

Hours:



Answer 1

lets come up with an equation that calculates the distance between trains at any given time

lets make d(t)=70 mph *(t) + 8 mph*(t)

We are trying to find t when the distance between the trains is 360 miles.

so we have 360=78*t

t=4.615 hours

Answer 2

Well after x hours the eastbound train will be 8x miles east of the start, and the westbound train 70x miles west of the start.

So distance between them is 8x + 70x = 360

Now solve for x