At 9 a.m., Luis started from City U and travelled towards City V and his speed remained constant throughout. At 10 a.m., Gwen started her journey from City U towards City V at an average speed of 72 km/h. Gwen overtook Luis at 3 p.m. After overtaking, Gwen carried on her journey at the same average speed and reached at City V at 3:45 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 3 p.m. = 5 h

Distance that Gwen had travelled until Gwen overtook Luis
= 5 x 72
= 360 km

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

Luis's average speed
= 360 ÷ 6
= 60 km/h

(b)
From 10 a.m. to 3:45 p.m. = 5 h 45 min

1 h = 60 min
5 h 45 min = 5 ⁴⁵ ₆₀
 h = 5 ³₄ h

Distance between the two cities
= 5 ³₄ x 72
= ²³₄ x 72
= 414 km

Answer(s): (a) 60 km/h; (b) 414 km