Question

Can anyone help me please ​

Answer 1

Step-by-step 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):

$\frac{2(y-4)}{y(y-4)} + \frac{4y}{y(y-4)} = \frac46$

since they now share a common denominator:

$\frac{2(y-4) + 4y}{y(y-4)} = \frac46$

$\frac{6y-8}{y(y-4)} = \frac46$

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.