Camera Issues. » Shutter speed

Ok, technical question here... I often seem to struggle to get fast shutter speeds when shooting outside in daylight. If I'm shooting landscapes at say f16, I only ever seem to be able to achieve 1/60sec or 1/100sec which can result in blurred images if I'm not using a tripod. If I open up to f3.5 I can get speeds a lot faster but this isn't an ideal aperture for landscapes as I need sharpness throughout the frame.
Do you think I have my camera set up wrongly or is this normal? What shutter speeds would you expect to achieve in daylight? Any help would be appreciated, thanks.

Jon