SOLUTION: Liz drove the first half of a trip at 36 mi/h. At what speed should she cover the remaining half in order to average 45 mi/h for the whole trip?

Question 408747: Liz drove the first half of a trip at 36 mi/h. At what speed should she cover the remaining half in order to average 45 mi/h for the whole trip?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
When you said "first half of a trip ", did you mean with respect to time or with respect to distance?
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Okay.
Let d = total distance.
Then for d/2 miles at 36 mph, his time was (d/2)/36 = d/72.
For the remaining d/2 miles at r mph, his time was (d/2)/r = d/(2r).
Total time of travel is hours.
Then we want
<==> <==>
==> ==> r = 60 mph, his rate at the 2nd half of the trip.
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