Stupid question - I think.

If your appliances were plumbed in by a professional, there shouldn't be a problem. I use mine at the same time. Most modern washing machines are cold fill and I think dishwashers have always been cold fill. As long as your mains pressure is normal there shouldn't be a shortage of water.

I often use both at the same time. The only problem is the noise!

I use mine at the same time too - I don't think they are using the water at the same time - once the dishwasher is full it takes forever to get to the next cycle anyway. I do tend to leave the washer until we've finished in the bathroom though as it does affect the water pressure supplying the shower.