A biker rode the first 20 miles of a trip at a constant rate

A biker rode the first 20 miles of a trip at a constant rate. For the next 16 miles, the biker reduced his speed by 2 mph. The total time for the 36 miles was 4 hours. Find the rate of the biker for each leg of his trip.

Solution

1st Part DATA:
distance = 20 mi ; rate = x mph ; time = d/r = 20/x hrs
-------------------
2nd Part DATA:
distance = 16 mi ; rate = (x-2) mph ; time = d/r = 16/(x-2) hrs
--------------------
EQUATION:
time + time = 4 hrs
(20/x) + (16/(x-2)) = 4
Divide thru by 4 to get:
(5/x) + 4/(x-2) = 1
Multiply thru by x(x-2) to get:
5(x-2) + 4x = x^2-2x
9x-10 = x^2-2x
x^2-11x+10 = 0
(x-10)(x-1) = 0
x = 10 or x = 1
Then x-2 = 8 mph or x-2 = -1
-----------
Only x-2=8 mph is realistic for the speed on the 2nd leg of the journey
So the speed on the 1st leg is 10 mph