At noon, a train leaves New York for Toronto while another leaves Toronto for New York. It takes one train hours and the other hours to make the trip. If both maintain constant speeds and travel along parallel tracks, at what time do they pass each other?

Source: NCTM Mathematics Teacher, October 2006

**Solution**

We use the following variables

= time (duration) in hours when the trains pass each other

= New York – Toronto distance in miles

= distance in miles from Toronto to the passing point

= distance in miles from New York to the passing point

We calculate speeds and distances

speed of slower train

speed of faster train

Divide both sides by d

= hours minutes

**Answer**: p.m.

**Alternative solution 1
**Suppose train 1 is slower than train 2. Since distance is proportional to time

is to as is to

hours