Question

Jon leaves his house for a business trip driving at a rate of 45 miles per hour. Half an hour later his wife, Emily, realizes he forgot his cell phone and begins to follow him at a rate of 55 miles per hour. How long will it take for Emily to catch Jon?

Answer 1

`135` minutes, or `2 1/4` hours.

Explanation:

We're looking for the point where Jon and Emily have travelled the same distance.

Let's say that Jon travels for time `t`, so he travels `45t` before his wife catches up.

Emily travels faster, at 55 mph, but she does travel for so long. She travels for `t-30`: `t` for the time her husband travels and `-30` to account for her late start.

That gives us:

`45t=55(t-30)`

`45t=55t-1650`

`10t=1650=>t=165` minutes

(we know it's minutes because I used `t-30` with the 30 being 30 minutes. I could have said `t-1/2` with `1/2` being half an hour)

So Jon travels 165 minutes, or `2 3/4` hours before Emily catches up.

Emily, for her part, travelled for `165-30=135` minutes, or `2 1/4` hours.

Pity Emily - she still has to drive home...