Answer: The answer is 1833 heads and 11 hours, 11 minutes.
Step-by-step explanation: Given that the Magic Dragon has 2013 heads. The brave Leo is cutting off the Dragon's heads at a speed of 5 heads per minute. But, the Dragon's heads are growing back at a speed of 2 heads per minute.
So, the number of heads of Dragon that are decreasing per minute = 3.
Therefore, after 1 hour, i.e., 60 minutes, The number of heads of the Dragon
= 2013 - 60 × 3 = 2013 - 180 = 1833 heads.
Now, the fight will last until all the heads of the Dragon are cut. Let the fight lasts for 'x' minutes, then
![2013-x\times 3=0\\\\\Rightarrow 3x=2013\\\\\Rightarrow x=\dfrac{2013}{3}=671.](https://tex.z-dn.net/?f=2013-x%5Ctimes%203%3D0%5C%5C%5C%5C%5CRightarrow%203x%3D2013%5C%5C%5C%5C%5CRightarrow%20x%3D%5Cdfrac%7B2013%7D%7B3%7D%3D671.)
Hence the fight lasts for 671 minutes, i.e., 11 hours and 11 minutes.
Thus, the Dragon will have 1833 heads after 1 hour and the fight will last for 11 hour and 11 minutes.