At 8 a.m., Valen started from City J and travelled towards City K and his speed remained constant throughout. At 10 a.m., Nora started her journey from City J towards City K at an average speed of 81 km/h. Nora overtook Valen at 2 p.m. After overtaking, Nora carried on her journey at the same average speed and reached at City K at 2:40 p.m.

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

(a)
From 10 a.m. to 2 p.m. = 4 h

Distance that Nora had travelled until Nora overtook Valen
= 4 x 81
= 324 km

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

Valen's average speed
= 324 ÷ 6
= 54 km/h

(b)
From 10 a.m. to 2:40 p.m. = 4 h 40 min

1 h = 60 min
4 h 40 min = 4 ⁴⁰ ₆₀
 h = 4 ²₃ h

Distance between the two cities
= 4 ²₃ x 81
= ¹⁴₃ x 81
= 378 km

Answer(s): (a) 54 km/h; (b) 378 km