Every morning Batman runs 5 miles then walks one mile He run

Every morning, Batman runs 5 miles, then walks one mile. He runs 6 mph faster than he walks. If his total time yesterday was 45 minutes, then how fast did he run? Clearly define your variable(s). Show your equations. ? all the numbers that must be excluded from the domain of the given function. ? = 3x + 1/2x^2 - 7x - 4 2x^2 + 7x - 8x - 4) (2x + 1) 4(2x + 1)

Solution

Let his speed be x mi/hr when he runs

So, while walking his speed = x- 6 mi/hr

Total time taken = 45min= 45/60 = 0.75 hrs

5/x +1/(x-6) =0.75

{5(x-6) +x}/x(x-6) =0.75

(6x -30) = 0.75(x^2 -6x)

-0.75x^2 + 10.5x -30 =0

Solve the quadratic equation to get Batman\'s speed while running and walking .

x = 4, 10

So, if we find speed while wolking = x- 6 = 4-6 = -2 which hasn no meaning

So, neglect the vaule x=4

So, solution he ran 10mi/hr and walked with 4mi/hr