SOLUTION: Say I'm in a car and travel 100 miles, then slow down by 5 miles per hour and travel 135 more. If the whole trip took 5 hours, how fast was I going on the first and second part?

Question 368796: Say I'm in a car and travel 100 miles, then slow down by 5 miles per hour and travel 135 more. If the whole trip took 5 hours, how fast was I going on the first and second part?
My issue is that I know how to solve this sort of problem quickly in my head, but I have no clue what the appropriate formula for solving it is. My new teacher is very strict about showing work and since I do all the work in my head there really isn't much to show. Can anyone go through this for me one step at a time, so that I might learn how to solve other problems like this?
The solution for the example above would be 50mph for the first two hours and 45mph for the next three. I'd just never be able to write out how I arrived at the answer.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
t = d / r ___ the total time is 5 hr

(100 / x) + [135 / (x - 5)] = 5
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