How does the reflex arc work without going to the brain?

The reflex arc is designed for quick, reactive movements that are instinctive. E.g. when we touch a hot pan, we need to react quickly otherwise our hand will get really badly burned. If the signal went from our fingers, all the way to the brain and then the muscles, this would take too long.The temperature receptors on our fingers detect heat, the stimulus, and the sensory neurones carry this signal to the spinal cord where it passes across a synapse to the relay neurones. Here a relay neurone (interneurone) transfers the circuit across another synapse (between two neurones) to the motor neurones. These will go on to make the muscles in our arm, the effectors, contract so we move our hand away from the pan.This on average should take 0.15 seconds.