When will the trains meet?

Question

Two cities A and B are 650 miles apart. Train #1 travels from City A to City B at 60 miles per hour. Train #2 travels from City B to City A at 70 miles per hour. Train #1 starts at 8:00 am from City A and Train #2 starts at 8:00 am from City B. What time will the two trains meet?

Answer 1

It REALLY helps to draw a picture so how about this:

Now lets see what it looks like when the trains meet:

If we say the distance Train 1 goes is "x", then the distance Train 2 has gone when they meet is "650 - x".

Distance = rate x time so:

time = Distance/rate or t = d/r

The time that goes by for train 1 will be the same time that has gone by for train 2 so d₁/r₁ = d₂/r₂ or:

x/60 = (650 - x)/70 now you can cross multiply to simplify.

70x = 60(650 - x)

70x = 39000 - 60x

130x = 39000

x = 300 miles

So since time = d₁/r₁ then time = 300/60 = 5 hours