SOLUTION: a man rode a bike for 12 mi and then hiked an additional 8 mi . the total time for the trip was 5 hr. if his rate when he was riding a bike was 10 mph faster than his rate walking

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Question 541143: a man rode a bike for 12 mi and then hiked an additional 8 mi . the total time for the trip was 5 hr. if his rate when he was riding a bike was 10 mph faster than his rate walking , which was each rate? i usally make a chart for problems like this
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Riding 12 miles
Hiking 8 miles

Riding x mph
Hiking x -10 mph
Total time 5 hours
Time forward 150 / x
Time return 150 / ( x -10 )

Time first part + time second part = 5 hours

12/x+8/(x-10)= 5
LCD = x*(x-10)
multiply the equation by the LCD
we get
12*(x-10)+8x= 5
12x-120 +8x=5X^2-50x
70x-120 =5X^2
5X^2-70 x+120= 0

/ 5
X^2 -14 x +24 =0
x^2-12x-2x+24=0
x(x-12)-2(x-12)=0
(x-12)(x-2)=0
x=12 OR 2
riding speed = 12 mph
Hiking speed = 2 mph
m.ananth@hotmail.ca