At 7 a.m., Luke started from City R and travelled towards City S and his speed remained constant throughout. At 10 a.m., Min started her journey from City R towards City S at an average speed of 88 km/h. Min overtook Luke at 1 p.m. After overtaking, Min carried on her journey at the same average speed and reached at City S at 2:15 p.m.

1. Find Luke'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 Min had travelled until Min overtook Luke
= 3 x 88
= 264 km

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

Luke's average speed
= 264 ÷ 6
= 44 km/h

(b)
From 10 a.m. to 2:15 p.m. = 4 h 15 min

1 h = 60 min
4 h 15 min = 4 ¹⁵ ₆₀
 h = 4 ¹₄ h

Distance between the two cities
= 4 ¹₄ x 88
= ¹⁷₄ x 88
= 374 km

Answer(s): (a) 44 km/h; (b) 374 km