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? 

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