SOLUTION: 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

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 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       Log On


   

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.
I know the average of the whole thing would be 5 mph.
I tried 5.5mph for the first 20 and 4.5 for the last 30 but the time I got is 10 hours 17 min.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Fx%2B30%2F%28x-1%29=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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
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