EricImasogie wrote:I have attached the question as an image. I started off by setting both the downstream and upstream equations to each other since they both have the same 'd' (distance) ( d = s * t ) .
Let's try that way.
We start with rate(r) * time(t) = distance(d), and get two equations.
(v - 3)(t + 1/2) = 90 and (v + 3)(t) = 90
Now we can set them equal to each other, because they both equal 90.
(v - 3)(t + 1/2) = (v + 3)(t)
Multiply it all out.
vt + v/2 - 3t - 3/2 = vt + 3t
Simplify.
v/2 - 3/2 = 6t
v - 3 = 12t
Now we can substitute the 12t for (v - 3) in the upstream equation and solve for t.
(12t)(t + 1/2) = 90 12t^2 + 6t = 90 2t^2 + t = 15 2t^2 + t - 15 = 0 (2t - 5)(t + 3) = 0
t = -3 or 2.5. Throw out the - 3, at least in this universe. Choose
A.
That's a fair amount of work. Wondering if there is a better way.
