At 8 a.m., Vincent started from City K and travelled towards City L and his speed remained constant throughout. At 9 a.m., Rachel started her journey from City K towards City L at an average speed of 90 km/h. Rachel overtook Vincent at 2 p.m. After overtaking, Rachel carried on her journey at the same average speed and reached at City L at 2:30 p.m.

1. Find Vincent's average speed in km/h.
2. What is the distance between the two cities?

(a)
From 9 a.m. to 2 p.m. = 5 h

Distance that Rachel had travelled until Rachel overtook Vincent
= 5 x 90
= 450 km

From 8 a.m. to 2 p.m. = 6 h

Vincent's average speed
= 450 ÷ 6
= 75 km/h

(b)
From 9 a.m. to 2:30 p.m. = 5 h 30 min

1 h = 60 min
5 h 30 min = 5 ³⁰ ₆₀
 h = 5 ¹₂ h

Distance between the two cities
= 5 ¹₂ x 90
= ¹¹₂ x 90
= 495 km

Answer(s): (a) 75 km/h; (b) 495 km