Question

A train leaves a station and travels north at a speed of 45 mph. Two hours later, a second train leaves on a parallel track and travels north at 75 mph. How far from the station will they meet?

Answer 1

`225` miles

Explanation:

If train `A` travels for `t` hours
and meets train `B` which will have been traveling for `t-2` hours
#{: (,ul("train "A),color(white)("xx"),ul("train "B)), ("time (hours):",t,,t-2), ("distance traveled (miles):",45 xx t,,75xx(t-2)) :}#

When they meet they will have traveled the same distance.
`color(white)("XXX")45t=75(t-2)`

`color(white)("XXX")rarr45t=75t-150`

`color(white)("XXX")rarr=150`

`color(white)("XXX")rarr t=5`

They will meet after `5` hours
at which point train `A` will have traveled `45xx5=225" miles"`
(and train `B` will also have traveled `75xx(5-2)=225" miles"`)