At 9 a.m., Cole started from City P and travelled towards City Q and his speed remained constant throughout. At 10 a.m., Hilda started her journey from City P towards City Q at an average speed of 90 km/h. Hilda overtook Cole at 3 p.m. After overtaking, Hilda carried on her journey at the same average speed and reached at City Q at 6:20 p.m.

1. Find Cole'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 Hilda had travelled until Hilda overtook Cole
= 5 x 90
= 450 km

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

Cole's average speed
= 450 ÷ 6
= 75 km/h

(b)
From 10 a.m. to 6:20 p.m. = 8 h 20 min

1 h = 60 min
8 h 20 min = 8 ²⁰ ₆₀
 h = 8 ¹₃ h

Distance between the two cities
= 8 ¹₃ x 90
= ²⁵₃ x 90
= 750 km

Answer(s): (a) 75 km/h; (b) 750 km