Time taken for battery to drain completely

It depends on how you use the device

I have a 24V 10Ah battery and a 200W (nominal) motor.

If I use the motor continually, and in a way where it is under moderate to high load, it will flatten the battery in about 45 minutes of use.

The problem with electric motors is that their rating does not tell you the minimum, maximum, or even average power consumed.

I know, for instance, if the motor is stalled, it will dissipate more than 200W (and the same if operating under a very heavy load). This is also not particularly good for it.

However, if running freely, it dissipates far less than 200W.

If the use is a motor on a bicycle, you typically see high power demand at low speed, reducing as speed increases. At higher speeds (unless geared in some way) the motor is likely to have far lower torque and consume far less than its rated power.

I will add that on my bike, the motor is connected via the gears, and I am able to keep it in a low-RPM, high torque, high power region. This is not true of hub motors. As has been stated, a lot has to do with your battery pack. I have a Lithium (LiFe I think) pack and it gives very good capacity at high discharge rates.