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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?

1 Answer

Answer:

#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...