Question

why vegitables cook quickly on oil rather than on water

Answer 1

Boiling Point of Oil is higher that Boiling Point of Water that's why food cooks quickly in Oil.

Answer 2

this mainly because of Oil heats to a higher temperature in normal use. It transfers heat from the stove heater to food much faster, higher temperature cooks the food much faster, its lower specific heat means the transfer is faster, and you use much less of it than water, so again, faster heat.