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_{p}t where r_{p} the rate of the passenger train
D_{p} = 80t
Let’s start with the freight train: D_{f} = r_{f}t 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
