The question reads "Alice and Bob, who are standing 6m apart, are trying to wrangle a bull. Each has a length of rope attached to the bull, with Alice's length being 3m and Bob's length being 4m. Alice observes at this instant that the distance between the bull and herself is decreasing at a rate of 0.1 m/s, while Bob observers that the distance between himself and the bull is increasing at 0.5 m/s. Where is the bull and in what direction is he running?"
My attempt:
Let A represent the distance from Alice and the bull
Let B represent the distance from Bob and the bull
$\frac{dA}{dt} = -0.1 m/s$
$\frac{dB}{dt} = 0.5 m/s$
I drew a triangle with side lengths 3, 4, 6.
$A = 3$
$B = 4$
Distance from Alice to Bob = 6
I'm not sure how to proceed from here however.
The triangle gives you where the bull is. I would put Alice at the origin and Bob at $(6,0)$. Then find the corner where the bull is. Now imagine the bull is running in direction $\theta$ from that point at speed $v$. If you project that vector on the vector from the bull to Bob you get $-0.5$. If you project it onto the vector from the bull to Alice you get $0.1$. You should get two equations in the unknown $\theta,v$ from this to solve.