Question 886482
A novice hiker can walk a 50 mile trail in 10 hr. the hiker traveled the first 20 miles of the trail at a constant rate before decreasing the rate by 1 mph. Find the rate for each part of the hike. 
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let x=rate 1st 20 mi
x-1=rate remaining 30 mi
travel time=distance/rate
..
{{{20/x+30/(x-1)=10}}}
lcd: x(x-1)
20(x-1)+30x=10(x^2-x)
20x-20+30x=10x^2-10x
10x^2-60x+20=0
x^2-6x+2=0
solve by quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
a=1, b=-6, c=2
ans:
x≈0.35 (reject, not reasonable)
or
x≈5.65
..
rate 1st 20 mi≈5.65 mph
rate remaining 30 mi≈4.65 mph