At 9 a.m., Paul started from City Z and travelled towards City A and his speed remained constant throughout. At 10 a.m., Hilda started her journey from City Z towards City A at an average speed of 84 km/h. Hilda overtook Paul at 1 p.m. After overtaking, Hilda carried on her journey at the same average speed and reached at City A at 1:25 p.m.

1. Find Paul'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 Hilda had travelled until Hilda overtook Paul
= 3 x 84
= 252 km

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

Paul's average speed
= 252 ÷ 4
= 63 km/h

(b)
From 10 a.m. to 1:25 p.m. = 3 h 25 min

1 h = 60 min
3 h 25 min = 3 ²⁵ ₆₀
 h = 3 ⁵₁₂ h

Distance between the two cities
= 3 ⁵₁₂ x 84
= ⁴¹₁₂ x 84
= 287 km

Answer(s): (a) 63 km/h; (b) 287 km