At 7 a.m., Luis started from City U and travelled towards City V and his speed remained constant throughout. At 10 a.m., Gem started her journey from City U towards City V at an average speed of 90 km/h. Gem overtook Luis at 1 p.m. After overtaking, Gem carried on her journey at the same average speed and reached at City V at 1:30 p.m.

1. Find Luis'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 Gem had travelled until Gem overtook Luis
= 3 x 90
= 270 km

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

Luis's average speed
= 270 ÷ 6
= 45 km/h

(b)
From 10 a.m. to 1:30 p.m. = 3 h 30 min

1 h = 60 min
3 h 30 min = 3 ³⁰ ₆₀
 h = 3 ¹₂ h

Distance between the two cities
= 3 ¹₂ x 90
= ⁷₂ x 90
= 315 km

Answer(s): (a) 45 km/h; (b) 315 km