A backpacker hiking into the wilderness area walked 9 miles

A backpacker hiking into the wilderness area walked 9 miles at a constant rate and then reduced this rate by 1 mph. Another 4 miles was hiked at this reduced rate. The time required to hike the 4 miles was 1 hour less than the time required to walk the 9 miles. Find the rate at which the hiker walked the first 9 miles.

Solution

1st segment DATA:
distance = 9 miles ; rate = x mph ; time = d/r = 9/x hrs
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2nd segment DATA:
distance = 4 miles ; rate = x-1 mph ; time = d/r = 4/(x-1) hrs
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Equation:
1st seg. time - 2nd seg. time = 1 hr
9/x - 4(x-1) = 1 hr
9(x-1) - 4x = x(x-1)
9x-9 - 4x = x^2-x
x^2 -6x +9 = 0
(x-3)^2 = 0
x = 3 mph (rate for the 1st segment)