SOLUTION: Each day, Amit runs nine miles and then walks one mile. He runs 10 mph faster than he walks. If his total time is 75 minutes, then what is Amit's running speed?

Question 282326: Each day, Amit runs nine miles and then walks one mile. He runs 10 mph faster than he walks. If his total time is 75 minutes, then what is Amit's running speed?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Each day, Amit runs nine miles and then walks one mile. He runs 10 mph faster than he walks. If his total time is 75 minutes, then what is Amit's running speed?
let him walk at x mph
he runs x+10 mph
time taken for running = 9/x+10
time he walks = 1/x
1/x+ 9/ x+10= 5/4 hours
x+10 +9x / x(x+10) = 5/4
10x+10= 5x(x+10) / 4
10x+10 = 5x^2 +50x /4
40x+40 = 5x^2 +50x
5x^2-10x-40=0
x^2-2x-8=0
x^2-4x +2x-8=0
x(x-4)+2(x-4)=0
(x+2)(x-4)=0
So x =4 mph walking speed
Running speed will be x+10 = 4+10 = 14 mph

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