At 8 a.m., Liam started from City G and travelled towards City H and his speed remained constant throughout. At 9 a.m., Tiffany started her journey from City G towards City H at an average speed of 78 km/h. Tiffany overtook Liam at 2 p.m. After overtaking, Tiffany carried on her journey at the same average speed and reached at City H at 1:40 p.m.

1. Find Liam's average speed in km/h.
2. What is the distance between the two cities?

(a)
From 9 a.m. to 2 p.m. = 5 h

Distance that Tiffany had travelled until Tiffany overtook Liam
= 5 x 78
= 390 km

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

Liam's average speed
= 390 ÷ 6
= 65 km/h

(b)
From 9 a.m. to 1:40 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 78
= ¹⁴₃ x 78
= 364 km

Answer(s): (a) 65 km/h; (b) 364 km