When does the cyclist get overtaken This question is not limited to any particular method; all methods accepted. This is a homework question, stated exactly as:

A cyclist starts off in a bike at an average speed of 16 km/h. 15 minutes later, a motorcyclist sets off on the same trail with an average speed of 48 km/h. How many minutes (in total) will the cyclist have ridden when he gets overtaken by the motorcycle?

I tried to form 2 simultaneous equations for the speed and distance of both but failed. Any help??

EDIT
Thanks for the retag, and you asked to me to show my working out. Knowing that the the first guy crossed d kilos in 15 minutes, we can work that out as 4. Now for the second guy, he would cross those 4 in only 5 minutes. So I tried to plot a linear relationship for each guy and solve for an intersection point, but since they both start at the origin (do they???) The only intersection is (0, 0). And if I try to start off guy#2 at 15 minutes, the intersection point is 30. The answer at the back of the book says 22.5

The speed of the cyclist is $3$ times slower than the speed of the motorcyclist. The motorcyclist, however goes after $15$ minutes from the same point. You can use number sense to figure this.
Or, when $x=$ amount in hours,
$16x=48(x-0.25)$, since the cyclist sets in $15$ minutes before the motorcyclist.
$0.25$ hours = $15$ minutes
$16x = 48x-12$
$-32x=-12$
$x=\cfrac {3}{8}$
The motorcyclist will overcome the cyclist after $\cfrac {3}{8}$ hours, or $22$ minutes and $30$ seconds.
