Question 408747
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/72 + d/(2r)}}} hours.
Then we want {{{d/(d/72 + d/(2r)) = 45}}}
<==> {{{1/(1/72 + 1/(2r)) = 45}}} <==> {{{1/72 + 1/(2r) = 1/45}}}
==> {{{1/(2r) = 1/120}}} ==> r = 60 mph, his rate at the 2nd half of the trip.