Roundup works by having the plant draw it down to the roots, so it is important that you get the application rate correct - if you use a solution that is too strong, the leaves will die too fast, and the roots will survive to fight another day. If the weeds are very big, this process takes a very long time.
You can do two things.
Use the application rate for a watering can, (you'll find it on the back of smaller bottles of Roundup), put a sponge on a long stick, and apply it that way, painting it on will break your heart, and you will probably splash yourself. Like all weedkillers, it is bad bad stuff.
If the weeds are very big, pull them, or cut them, and catch the regrowth. The smaller plants are easier and faster to permanently kill.