math! please helP!?

Question

A horse travels 40km per hour faster than a mule. The horse goes 360km in 2hrs less time than the mule goes 360km., Find the speed of each animal.
[show the solution step by step]

here's the equation:
360/(x+40) =360/(x) - 3

Answer 1

Where is the '-3' from?

This is how i would do it
let the speed of the mule be x
therefore speed of horse is 40+x
[360/(40+x)]+2 = 360/x
360/(40+x) = (360/x) - 2
360/(40+x) = (360/x) - 2x/x
360/(40+x) = (360-2x)/x
360x = (40+x)(360-2x)
360x = 14400 - 80x + 360x - 2x^2
2x^2 + 80x - 14400 = 0
x^2 +40x - 7200 = 0
x = {-b +- [b^2 - 4ac]^(1/2) } / 2a
x = {-40 +- [(40)^2 - 4(1)(-7200)]^(1/2) } / 2
x = {-40 +- [30400]^(1/2) } / 2
x = {-40 +- 174.3559577 } / 2
x = 67.17797887 or -107.1779789(N.A. as speed cant be -ve)
Mule's speed is 67.17797887 km/h
Horse's speed is 67.17797887 + 40 = 107.17797887km/h

+- means plus minus
I dint round up any values. You may want to in your working.

Answer 2

let the speed of mule be x and the speed of horse be 40+x

therefore the time taken by the mule to travel 360 km will be 360/x, and the time taken by the horse to travel 360 km will be 360/(x+40). [Because time=distance/speed]

so,

360/(x+40)=360/x-2
or, 360/(x+40)=(360-2x)/x
or, 360x=(x+40)(360-2x)
or, 360x= 360x+14400-2x^2-80x
or, 2x^2+80x-360x+360x-14400=0
or, 2x^2+80x-14400=0
or, x^2+40x-7200
Solving this equation we get,
Either,
x=-107.18
or,
x=67.18

As speed cannot be negative, x= 67.18

therefore, x+40=107.18


so, the speed of the mule is 67.18 km/hr and the speed of the horse is 107.18 km/hr

Answer 3

Here's the correct equation:
360/(x+40) =360/(x) - 2

360x = 360(x + 40) - 2(x)(x+40)
360x = 360x + 14400 - 2x^2 - 40x
2x^2 + 40x - 14400 = 0
x^2 + 20x - 7200 = 0

stuff that into the quadradic equation and get your answer