## Crossing Trains

#### Problem

A train travels a distance of 90 miles from A to B in one hour. Another train sets off at the same time and travels from B to A, taking two hours to complete the journey.

How many miles from A did the two trains cross?

#### Solution

As the first train completed the journey in half the time of the second train it must have travelled twice as fast. So when the two trains crossed the first train would have travelled twice as far and would have completed ^{2}/_{3} of the journey. Hence both trains were ^{2}/_{3} of 90 = 60 miles from A.

What if the first train takes 2 hours and the second train takes 3 hours to complete the journey?

Can you generalise?

Problem ID: 96 (Jan 2003) Difficulty: 1 Star