SOLUTION: Amanda drove 50 miles. She decreased her speed by 20 mph and drove another 5 miles. If the entire trip took one hour and thirty minutes, at what rate(s) did Amanda drive?
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Question 509517: Amanda drove 50 miles. She decreased her speed by 20 mph and drove another 5 miles. If the entire trip took one hour and thirty minutes, at what rate(s) did Amanda drive? Answer by solver91311(24713) (Show Source):
Use time equals distance divided by rate. Let represent the initial rate. Then the reduced rate is . Let represent the time it took to travel the first 50 miles. Then is the time it took to travel the last 5 miles.
We know that
and
Substituting from the first equation:
A little Algebra music, Sammy:
Multiply by 2 and the quadratic factors rather tidily. One of the roots doesn't work because it is less than 20, which means that the rate would be negative (driving in reverse to go backwards in time?) for the 5 mile second leg of the trip.
Solve for and then calculate
John
My calculator said it, I believe it, that settles it
