Water Gun Race - Is it doable?

PeterH:
I suggest you start by deciding what sort of water pressure and maximum volume flow rate you need, then spec the water supply for that.

This cannot be overstated.

if you have one nozzle, you could get high pressure and high volume.
if you have 10 nozzles, the flow could decrease to be unusable.

the end result should be that there is no change on any unit, regardless how many are in use.

the rest is beginners stuff to a large degree. solenoids and relays and switches and some programming.

it would be easy enough to buy a valve from home depot and connect it with a foot switch to try it out. get multiple nozzles and see how they change pressure with increasing quantity of nozzles.

I would highly suggest that you use a GFI and make sure the ground on the extension cord is working. do not consider that as your first line of protection. if it ever does trip, re-evaluate your installation to make things safe.