Now, the student speeds up.
And we know that
Start by putting the mass relation in equations 1 and 2.
(1) <-- Cancel the
(2) <-- Cancel the
Note that the RHS of both equation 1 and equation 2 are the same. Thus the LHS of equation 1 and equation 2 are also the same.
You can solve this using the quadratic formula. I get that
or . Now the v quantities in these equations are speeds, which are always positive or zero. So we discard the negative solution.