At 05 15, Rachel left Town Y and cycled towards Town Z. Xylia left Town Y and cycled towards Town Z at 05 45. Xylia's cycling speed was 2 km/h faster than Rachel. At 13 15, Xylia caught up with Rachel. Find the cycling speed of each cyclist.

1. Rachel
2. Xylia

(a)
Duration that Xylia cycled from 05 45 to 13 15
= 7³⁰₆₀
= 7¹₂ h

Distance that Xylia cycled more than Rachel
= 7¹₂ x 2
= 15 km

However, since Rachel left 30 minutes earlier than Xylia and Xylia caught up with Rachel, it means that Rachel has cycled 15 km in 30 min.

1 h = 60 min 
30 min = 30 ÷ 60 = ¹₂ h

Rachel's cycling speed
= 15 ÷ ¹₂
= 15 x ²₁
= 30 km/h

(b)
Xylia's cycling speed
= 30 + 2
= 32 km/h

Answer(s): (a) 30 km/h ; (b) 32 km/h