At 9 a.m., Valen started from City N and travelled towards City P and his speed remained constant throughout. At 10 a.m., Penelope started her journey from City N towards City P at an average speed of 84 km/h. Penelope overtook Valen at 3 p.m. After overtaking, Penelope carried on her journey at the same average speed and reached at City P 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 3 p.m. = 5 h

Distance that Penelope had travelled until Penelope overtook Valen
= 5 x 84
= 420 km

From 9 a.m. to 3 p.m. = 6 h

Valen's average speed
= 420 ÷ 6
= 70 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 84
= ¹⁴₃ x 84
= 392 km

Answer(s): (a) 70 km/h; (b) 392 km