At 8 a.m., Pierre started from City H and travelled towards City J and his speed remained constant throughout. At 10 a.m., Yen started her journey from City H towards City J at an average speed of 78 km/h. Yen overtook Pierre at 2 p.m. After overtaking, Yen carried on her journey at the same average speed and reached at City J at 3:30 p.m.

1. Find Pierre'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 Yen had travelled until Yen overtook Pierre
= 4 x 78
= 312 km

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

Pierre's average speed
= 312 ÷ 6
= 52 km/h

(b)
From 10 a.m. to 3:30 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 78
= ¹¹₂ x 78
= 429 km

Answer(s): (a) 52 km/h; (b) 429 km