If the brain sends a signal to move what's the time it takes the signal to travel via neurons to motor neurons in hands, arms and legs?
How fast do those signals travel?
Speed of transmission is going to vary depending on the neuron fiber subtype.
Specifically, the biggest gains will be seen with cross-sectional area (feel free to ask why on physics.stackexchange.com) and neurons with myelin sheathes (fat wrappings which affect saltatory conduction rates).
You're specifically asking about Efferent neuron transmission rates, but here's a general idea:
Keep in mind that the entire circuit (from pre-motor cortex to muscle spindles) will involve several different types. In-general, your central nervous system (brain, brain-stem, spinal chord) are A-alpha, and if I recall correctly - the somatic nervous system (the voluntarily-activated neurons throughout the rest of your body in the PNS [peripheral nervous system]) are A-delta. If I'm wrong, somebody please correct me.
On average non-voluntary reflexes (which is actually information going to the CNS, being processed, and then going out to the motor neurons) take about 0.3 seconds. However, the average human can blink in about 0.1 seconds, which is probably a better measure.
It is generally not a one-way process. The lag also depends on which frequencies you look at (the brain and limbs kind of speak using several channels at the same time). Near 10 Hz the lag is few dozen milliseconds.
Look for articles about EMG and EEG (or MEG) coupling for more precise info.
Use the paper http://homes.mpimf-heidelberg.mpg.de/~mhelmsta/pdf/2002%2520MEG%2520muscle%2520Review.pdf as a starting point.
PS. There is no neurons in limbs