Velocity in applications of integration The question reads as this:
Person A starts riding a bike at noon (t=0) from Niwot to Berthoud, a distance of 20km, with velocity $v(t)=15/(t+1)^2$.
Person B starts riding a bike at noon as well (t=0) from Berthoud to Niwot with velocity $u(t)=20/(t+1)^2$
Assume distance is measured in kilometers amd time is in hours.
A. Make a graph of Person A's distance to Niwot as a function of time
B. Make a graph of Person B's distance to Berthoud as a function of time.
C. How far has each person traveled when they meet? When do they meet?
D. More generally, if the rider's speeds are $v(t)=A/(t+1)^2$ and $u(t)=B/(t+1)^2$ and the distance between the towns is D, what conditions on A,B,and D must be met to ensure the riders pass each other?
E.With the velocity functions given in part(d), make a conjecture about the maximum distance each person can ride, given unlimited time.
So when I started this problem, I first took the antiderivative of both velocity functions to get their respective position functions, getting $v(t)=-15/(t+1)$ and $u(t)=-20/(t+1)$. But if the position of each is set to 20 (20km to their destinations, the result I get in time is a negative number for both. Also, the two position functions never actually intersect, making me believe that the two riders never actually pass each other at one point. If anyone could help me find a way to approach this problem, it would be greatly appreciated.

Let's say that Niwot is at (0,0) and Berthoud is at (20,0) giving the following:
$$A.)\quad P_v = \int_{0}^{t} V_{vt} = \int_{0}^{t}\frac{15\,dt}{(t+1)^2} = \frac{15t}{t+1}$$
$$B.) \quad  P_u = 20 - \int_{0}^{t} V_{ut} = 20 -\int_{0}^{t}\frac{20\,dt}{(t+1)^2} = 20-\frac{20t}{t+1}$$
$$C.) \quad P_u = P_v\,\, \therefore \,\,\frac{15t}{t+1} = 20-\frac{20t}{t+1}\,\, \therefore \,\, t = \frac{4}{3}$$
I am fairly certain these are correct, but I haven't checked my work very much... some fact checking would be nice! I'm relying on the fact that distance covered from $t=a$ to $t=b$ is $\int_{a}^{b} v_x dt$
