Question

I have attached the screenshots of the questions

Answer 1

Explanation:

(a)

`\boxed{time=(distance)/(speed) }`

Route A:

`t=(800)/(x) \ days`

Route B:

`t=(800)/(x-5) \ days`

Route C:

`t=((800+100))/(x+5)`

`=(900)/(x+5) \ days`

(b)

`t_B-t_C=20`

`(800)/(x-5) -(900)/(x+5) =20`

`(800(x+5))/((x+5)(x-5)) -(900(x-5))/((x+5)(x-5)) =(20(x+5)(x-5))/((x+5)(x-5))`

`800(x+5) -900(x-5) =20(x+5)(x-5)`

`800x +4000-900x+4500=20x^(2) -500`

`20x^(2) +100x-9000=0`

`x^(2) +5x-450=0`

(c)

`\boxed{x=(-b\pm√(b^2-4ac) )/(2a) }`

`x=(-5\pm√(5^2-4(1)(-450)) )/(2(1))`

`=18.9\ days`

(answer must be in positive numbers, so -23.9 days is not valid