Two trains, two different stations 300 km apart

Question

At 3:15 train A departs from station X at an eastward speed of 70 kph. At the same time, train B departs from station Y which is 300 km east of station X, headed westward at 50 kph. At what two times will trains A and B be 90km apart?

Answer 1

First let’s set up the distances from station X. Let d_A and d_B be the distance of train A and B respectively from station X.

Since train A moves at 70 kilometers per hour, let t be the number of hours after 3:15pm.

d_A=70t

and

Since train B moves at 50 kilometers per hour in the opposite direction and it starts 300 kilometers away from station X

d_B=300-50t

Now, the setup is complete. We now need to find when

d_A-d_B=90. Why? Because this is when the relative distances between the trains is 90 kilometers.

d_A-d_B=70t-(300-50t)

d_A-d_B=120t-300

and using d_A-d_B=90

90=120t-300

390=120t

3.25=t

Thus, 3.25 hours after 3:15 pm, the two trains will be 90 kilometers apart: alternatively you can just say 6:30 pm the trains will be 90 kilometers apart. Hope this helps!