At 09 20, Cathy left Town K and cycled towards Town L. Esther left Town K and cycled towards Town L at 09 50. Esther's cycling speed was 2 km/h faster than Cathy. At 15 20, Esther caught up with Cathy. Find the cycling speed of each cyclist.

1. Cathy
2. Esther

(a)
Duration that Esther cycled from 09 50 to 15 20
= 5³⁰₆₀
= 5¹₂ h

Distance that Esther cycled more than Cathy
= 5¹₂ x 2
= 11 km

However, since Cathy left 30 minutes earlier than Esther and Esther caught up with Cathy, it means that Cathy has cycled 11 km in 30 min.

1 h = 60 min 
30 min = 30 ÷ 60 = ¹₂ h

Cathy's cycling speed
= 11 ÷ ¹₂
= 11 x ²₁
= 22 km/h

(b)
Esther's cycling speed
= 22 + 2
= 24 km/h

Answer(s): (a) 22 km/h ; (b) 24 km/h