Let speed of B = x m/s. Then speed of A = (x + 1) m/s.

Formula: Time = \frac{\text{distance}}{\text{speed}}

Time of B = \frac{180}{\text{x}},

Time of A = \frac{180}{\text{x + 1}}.

Given time difference 2 s:

\frac{180}{\text{x}} − \frac{180}{\text{x + 1}} = 2.

180 × (\frac{1}{\text{x}} − \frac{1}{\text{x+1}}) = 2

⇒ 180 × \frac{\text{x+1 − x}}{\text{x(x+1)}} = 2

⇒ \frac{180}{\text{x(x+1)}} = 2

⇒ x(x+1) = 180/2 = 90.

Hence x² + x − 90 = 0.

⇒ x² + (10 – 9)x − 90 = 0

⇒ x² + 10x – 9x − 90 = 0

⇒ (x + 10)(x – 9) = 0

x = 9 or x = -10 (reject)

Therefore speed of B = 9 m/s.