At 9 a.m., Xavier started from City N and travelled towards City P and his speed remained constant throughout. At 10 a.m., Diana started her journey from City N towards City P at an average speed of 72 km/h. Diana overtook Xavier at 1 p.m. After overtaking, Diana carried on her journey at the same average speed and reached at City P at 2:35 p.m.

1. Find Xavier'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 Diana had travelled until Diana overtook Xavier
= 3 x 72
= 216 km

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

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

(b)
From 10 a.m. to 2:35 p.m. = 4 h 35 min

1 h = 60 min
4 h 35 min = 4 ³⁵ ₆₀
 h = 4 ⁷₁₂ h

Distance between the two cities
= 4 ⁷₁₂ x 72
= ⁵⁵₁₂ x 72
= 330 km

Answer(s): (a) 54 km/h; (b) 330 km