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):
[tex]\frac{2(y-4)}{y(y-4)} + \frac{4y}{y(y-4)} = \frac46[/tex]
since they now share a common denominator:
[tex]\frac{2(y-4) + 4y}{y(y-4)} = \frac46[/tex]
[tex]\frac{6y-8}{y(y-4)} = \frac46[/tex]
cross-products:
[tex]6 (6y-8) = 4y(y-4)[/tex]
further simplification:
[tex]36y - 48 = 4y^2 - 16y[/tex]
[tex]4y^2 - 52y + 48 = 0[/tex]
[tex]y^2 - 13y + 12 = 0[/tex]
q.e.d.
