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?

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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) About Me  (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 d%2F72+%2B+d%2F%282r%29 hours.
Then we want d%2F%28d%2F72+%2B+d%2F%282r%29%29+=+45
<==> 1%2F%281%2F72+%2B+1%2F%282r%29%29+=+45 <==> 1%2F72+%2B+1%2F%282r%29+=+1%2F45
==> 1%2F%282r%29+=+1%2F120 ==> r = 60 mph, his rate at the 2nd half of the trip.