I have a Cannondale Quick CX3 and it has a 700C X 40 tire. I am researching options to replace my tire (better quality, different size than what came standard on the bike) and inner tube (with Slime filled in it). However, the slime filled tubes come in smaller widths.

Here’s my question: I’d like to replace my existing Kenda Tire/Tube with the following :
  • Schwalbe Marathon Plus Bike Tire - 700 x 28 / 32 / 35 - Item #108439
  • Slime Self-Sealing Smart Presta Tube - 700 x 28-35 - Item #732121

Will the above tire/tube combination work with my existing Rims as-is or should I buy new Rims as well ?

Thank you for your help. Please advise.