Question

Two passenger trains started at the same time from towns 238 miles apart and met in 3 hours. The rate of one train was 6 mph slower than that of the other. What is the rate for both trains?

Answer 1

The trains are moving at `36 2/3` `mph` and `42 2/3` `mph`.

Explanation:

The two trains are `238` miles apart. As the difference in speed is `6mph` and they meet in `3` hours, they cannot be travelling in same direction.

In other words, they are travelling towards each other and if their speed is `x` `mph` and `x+6` `mph` respectively, they arecoming neareach other `x+x+6=2x+6` miles per hour.

And in `3` hours, they will come `3xx(2x+6)` miles closer. As they meet in `3` hours, we must have

`3xx(2x+6)=238` or `6x+18=238`

i.e. `6x=238-18=220`

and `x=220/6=110/3=36 2/3` `mph`

and other train iss travelling at `36 2/3+6=42 2/3` `mph`