Rate problem. Could someone give a detailed explanation on how to solve this the right way

A driver covers the first 70% of a distance at an average speed of 67 mph. At what speed must she drive the remainder of the distance so as to average 55 mph for the entire trip?

Let D = the length of the total trip.
Let r be the rate of speed for the remaining 30% of the trip.

D*55 = ((7D/10) * 67) + ((3D/10) * r).............Divide both sides by D

55 = 46.9 + 3r/10....................Multiply both sides by 10

550 = 469 + 3r

3r = 550 - 469 = 81

Divide both sides by 3.

r = 27 <----------- Answer (rate of speed for last 30%)

Let's check:

(0.7 * 67) + (0.3 * 27) = 46.9 + 8.1 = 55

The check is valid and the answer is correct.

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