At 7 a.m., Luke started from City U and travelled towards City V and his speed remained constant throughout. At 10 a.m., Elyse started her journey from City U towards City V at an average speed of 86 km/h. Elyse overtook Luke at 1 p.m. After overtaking, Elyse carried on her journey at the same average speed and reached at City V at 4:30 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 Elyse had travelled until Elyse overtook Luke
= 3 x 86
= 258 km

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

Luke's average speed
= 258 ÷ 6
= 43 km/h

(b)
From 10 a.m. to 4:30 p.m. = 6 h 30 min

1 h = 60 min
6 h 30 min = 6 ³⁰ ₆₀
 h = 6 ¹₂ h

Distance between the two cities
= 6 ¹₂ x 86
= ¹³₂ x 86
= 559 km

Answer(s): (a) 43 km/h; (b) 559 km