At 06 20, Vanessa left Town X and cycled towards Town Y. Kathy left Town X and cycled towards Town Y at 06 50. Kathy's cycling speed was 2 km/h faster than Vanessa. At 13 20, Kathy caught up with Vanessa. Find the cycling speed of each cyclist.

1. Vanessa
2. Kathy

(a)
Duration that Kathy cycled from 06 50 to 13 20
= 6³⁰₆₀
= 6¹₂ h

Distance that Kathy cycled more than Vanessa
= 6¹₂ x 2
= 13 km

However, since Vanessa left 30 minutes earlier than Kathy and Kathy caught up with Vanessa, it means that Vanessa has cycled 13 km in 30 min.

1 h = 60 min 
30 min = 30 ÷ 60 = ¹₂ h

Vanessa's cycling speed
= 13 ÷ ¹₂
= 13 x ²₁
= 26 km/h

(b)
Kathy's cycling speed
= 26 + 2
= 28 km/h

Answer(s): (a) 26 km/h ; (b) 28 km/h