At 8 a.m., Rael started from City X and travelled towards City Y and his speed remained constant throughout. At 9 a.m., Lucy started her journey from City X towards City Y at an average speed of 90 km/h. Lucy overtook Rael at 1 p.m. After overtaking, Lucy carried on her journey at the same average speed and reached at City Y at 2:50 p.m.

1. Find Rael's average speed in km/h.
2. What is the distance between the two cities?

(a)
From 9 a.m. to 1 p.m. = 4 h

Distance that Lucy had travelled until Lucy overtook Rael
= 4 x 90
= 360 km

From 8 a.m. to 1 p.m. = 5 h

Rael's average speed
= 360 ÷ 5
= 72 km/h

(b)
From 9 a.m. to 2:50 p.m. = 5 h 50 min

1 h = 60 min
5 h 50 min = 5 ⁵⁰ ₆₀
 h = 5 ⁵₆ h

Distance between the two cities
= 5 ⁵₆ x 90
= ³⁵₆ x 90
= 525 km

Answer(s): (a) 72 km/h; (b) 525 km