At 9 a.m., Archie started from City M and travelled towards City N and his speed remained constant throughout. At 10 a.m., Raeann started her journey from City M towards City N at an average speed of 72 km/h. Raeann overtook Archie at 1 p.m. After overtaking, Raeann carried on her journey at the same average speed and reached at City N at 6:30 p.m.

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

(a)
From 10 a.m. to 1 p.m. = 3 h

Distance that Raeann had travelled until Raeann overtook Archie
= 3 x 72
= 216 km

From 9 a.m. to 1 p.m. = 4 h

Archie's average speed
= 216 ÷ 4
= 54 km/h

(b)
From 10 a.m. to 6:30 p.m. = 8 h 30 min

1 h = 60 min
8 h 30 min = 8 ³⁰ ₆₀
 h = 8 ¹₂ h

Distance between the two cities
= 8 ¹₂ x 72
= ¹⁷₂ x 72
= 612 km

Answer(s): (a) 54 km/h; (b) 612 km