At 7 a.m., Elijah started from City D and travelled towards City E and his speed remained constant throughout. At 9 a.m., Lucy started her journey from City D towards City E at an average speed of 69 km/h. Lucy overtook Elijah at 1 p.m. After overtaking, Lucy carried on her journey at the same average speed and reached at City E at 5:40 p.m.

1. Find Elijah'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 Elijah
= 4 x 69
= 276 km

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

Elijah's average speed
= 276 ÷ 6
= 46 km/h

(b)
From 9 a.m. to 5:40 p.m. = 8 h 40 min

1 h = 60 min
8 h 40 min = 8 ⁴⁰ ₆₀
 h = 8 ²₃ h

Distance between the two cities
= 8 ²₃ x 69
= ²⁶₃ x 69
= 598 km

Answer(s): (a) 46 km/h; (b) 598 km