At 8 a.m., Jack started from City H and travelled towards City J and his speed remained constant throughout. At 10 a.m., Vanessa started her journey from City H towards City J at an average speed of 81 km/h. Vanessa overtook Jack at 2 p.m. After overtaking, Vanessa carried on her journey at the same average speed and reached at City J at 3:40 p.m.

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

(a)
From 10 a.m. to 2 p.m. = 4 h

Distance that Vanessa had travelled until Vanessa overtook Jack
= 4 x 81
= 324 km

From 8 a.m. to 2 p.m. = 6 h

Jack's average speed
= 324 ÷ 6
= 54 km/h

(b)
From 10 a.m. to 3:40 p.m. = 5 h 40 min

1 h = 60 min
5 h 40 min = 5 ⁴⁰ ₆₀
 h = 5 ²₃ h

Distance between the two cities
= 5 ²₃ x 81
= ¹⁷₃ x 81
= 459 km

Answer(s): (a) 54 km/h; (b) 459 km