Let,

Speed of the boat in still current = x km/h

Given,

Speed of the stream = 3 km/h

Speed of boat along the current = (x + 3) km/h

Speed of boat against the current = (x - 3) km/h

Given,

Boat goes 55 km and comes back in 16 hours

= [55/(x + 3)] + [55/(x - 3)] = 16

⇒ 110x/(x² - 9) = 16

⇒ 110x = 16x² - 144

⇒ 8x² - 55x - 72 = 0

⇒ 8x² - 64x + 9x - 72 = 0

⇒ 8x(x - 8) + 9(x - 8) = 0

⇒ (x - 8)(8x + 9) = 0

⇒ x - 8 = 0 or 8x + 9 = 0

⇒ x = 8 or x = - 9 /8

? Speed can’t be negative

∴ x = 8 km/hr