At 7 a.m., Liam started from City X and travelled towards City Y and his speed remained constant throughout. At 8 a.m., Yoko started her journey from City X towards City Y at an average speed of 90 km/h. Yoko overtook Liam at 1 p.m. After overtaking, Yoko carried on her journey at the same average speed and reached at City Y 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 8 a.m. to 1 p.m. = 5 h

Distance that Yoko had travelled until Yoko overtook Liam
= 5 x 90
= 450 km

From 7 a.m. to 1 p.m. = 6 h

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

(b)
From 8 a.m. to 1:40 p.m. = 5 h 40 min

1 h = 60 min
5 h 40 min = 5 ⁴⁰ ₆₀
 h = 5 ²₃ h

Distance between the two cities
= 5 ²₃ x 90
= ¹⁷₃ x 90
= 510 km

Answer(s): (a) 75 km/h; (b) 510 km