120 F bucket of H20 on a 90 F rock

The rock would, as most rocks do, act like a big heat sink and draw heat away from the bucket until the temps equalized.
Joe

Would the rock cause the water to reach room temperature faster or slower?-

If the rock is a poor conductor or has an irregular surface, the loss of heat may be slower.

Are we to assume a vacuum for the experiment? If so, the water would begin to boil almost immediately, and continue to do so till the water froze.

Mostly good answers. If this is a copper or silver bucket making the same area of contact with the rock as the air to bucket contact, the rock would control the water temperature almost as much as the air would control the water temperature; otherwise the rock is almost irrelevent, as rock to water heat conduction is poor.
Another problem is the bottom inch of water would cool to perhaps 95 degrees f, but would not mix with the lighter warmer water above until (and if) the air and evaporation cooled the water surface below 95 degrees f as there would be no convection with the bottom inch of water.
I said "and if" as the air temperature could be 100 degrees f. In this latter case the water near the top would likely never cool below 95 degree f as the surface of the rock in contact with the bucket would be about 95 degrees f even if the rock was big enough to stay at 90 degrees f an inch below the rock's surface, forever. This because most kinds of rock are rather poor conductors of heat. Neil

I read the question again. The air would
dominate unless we are in a vacuum.
No air and no light (including infrared)
means the ambient temperature is
minus 460 rankine = -273 C = absolute
zero, so the rock at any temperature
would slow the cooling of the water as
the bucket could not radiate the heat
away as efficiently in the direction of the
rock. I can't think of any way to prevent
the rock from radiating infrared light at
the bucket of water, so this radiation
would further slow the cooling of the
water, but not by much. Neil

Who knew! I can always count on a good answer from able2know. Dov