Question

Can anyone help me please ​

Answer 1

Explanation:

Realize that:

speed = distance / time and thus

time = distance / speed

Then the whole journey of 40/60 hours is the sum of (let's call them t1 and t2)

cycling: t1 = 2/y hours

running: t2 = 4/(y-4) hours

so we must simplify t1+t2=40 minutes (a.k.a. 4/6 hours):

2/y + 4/(y-4) = 4/6

let's multiply the first term by (y-4)/(y-4) and the second term by (y/y):

`(2(y-4))/(y(y-4)) + (4y)/(y(y-4)) = \frac46`

since they now share a common denominator:

`(2(y-4) + 4y)/(y(y-4)) = \frac46`

`(6y-8)/(y(y-4)) = \frac46`

cross-products:

`6 (6y-8) = 4y(y-4)`

further simplification:

`36y - 48 = 4y^2 - 16y`

`4y^2 - 52y + 48 = 0`

`y^2 - 13y + 12 = 0`

q.e.d.