TRAIN PROBLEM PART 2

We will look at two trains leaving from DIFFERENT stations in this paper.

Distance = rate x time is our basic formula to start.

Problem: A train passenger train leaves from Station A traveling at a rate of 80 mph. A freight train leaving Station B travels at a rate of 20 mph from a different train track. These two railroad stations are 1200 miles apart. When will these two trains pass each other and how far from EACH station will they be when they pass each other?

Solution: The problem has three parts to the solution. 1) The TIME it took for the trains to pass each other, 2) The DISTANCE the passenger train traveled when the two trains pass each other and 3) The DISTANCE the freight train traveled when the two trains pass each other.

Remember, both trains are in motion the SAME amount of time before they pass each other so we’ll just use “t” to represent the time it takes them to pass.

Let’s start with the passenger train: D_p = r_pt where r_p the rate of the passenger train

D_p = 80t

Let’s start with the freight train: D_f = r_ft where r_t the rate of the freight train

D_f = 20t

The TOTAL distance (D_T) the two train stations are apart is 1200 miles. This distance will also equal the part the passenger train travels (D_p) + the distance the freight train travels (D_f) so:

    D_T = D_p  +  D_f

1200 = 80t + 20t

Combine like terms to obtain:

1200 = 100t

Divide BOTH sides by 100:

1200 = 100t

  100    100

12 = t

So, the TIME it took for the trains to pass each other was 12 hours.

The DISTANCE the passenger train traveled from its’ station was:

D_p = 80t

D_p = 80(12)

D_p = 960 miles

The DISTANCE the freight train traveled from its’ station was:

D_f = 20t

D_f = 20(12)

D_f = 240 miles