# SOLUTION: a man rode a bycycle for 12 miles then hiked an additional 8 miles . the total time for the trip was 5 hrs . if the rate when he was riding his bicycle was 10 miles per hour faster

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 Question 110068: a man rode a bycycle for 12 miles then hiked an additional 8 miles . the total time for the trip was 5 hrs . if the rate when he was riding his bicycle was 10 miles per hour faster than his rate walking , what was each rate Answer by stanbon(57290)   (Show Source): You can put this solution on YOUR website!a man rode a bycycle for 12 miles then hiked an additional 8 miles . the total time for the trip was 5 hrs . if the rate when he was riding his bicycle was 10 miles per hour faster than his rate walking , what was each rate ------------ Bike DATA: distance = 12 miles ; rate= x mph ; time = d/r = 12/x hrs ---------------- Walk DATA: distance = 8 miles ; rate = x-10 mph ; time = d/r = 8/(x-10) hrs -------------------- EQUATION: time + time = 5 hrs. 12/x + 8/(x-10) = 5 3/x + 2/(x-10) = 5/4 [3x-30+2x] = (5/4)x(x-10) 5x-30 = (5/4)x(x-10) x-6 = [x^2-10x)/4 x^2-10x = 4x-24 x^2-14x+24=0 x^2-2x-12x+24=0 x(x-2)-12(x-2)=0 (x-2)(x-12)=0 x = 2 or x = 12 Positive answer: x-10 = 2 mph (walking rate) x=12 mph (biking rate) ================== Cheers, Stan H.