A pest control person uses a particular machine for his job, it moves along the circumference of a circular hall of radius 49 metres in 148 minutes to finish the pest control. How many minutes more will it take him to move along the perimeter of a hexagon of side 54 metres?

Distance covered by the pest control person = Circumference of the circular hall = $$2*\frac{22}{7}*49$$ = 308 m

So machine's speed = $$\frac{308}{148}$$ m/min = 2.08 m/min

The distance that is to be covered =  Perimeter of hexagon = 6 * 54 = 324 m

Time consumed  = $$\frac{Distance}{Speed}$$

                           = $$\frac{324}{2.08}$$ 

                           =155.7 min

So additional time taken by the machine is = 155.7-148 = 7.7 $$\approx$$ 7.69 minutes.