At 7 a.m., Ken started from City F and travelled towards City G and his speed remained constant throughout. At 10 a.m., Rachel started her journey from City F towards City G at an average speed of 84 km/h. Rachel overtook Ken at 1 p.m. After overtaking, Rachel carried on her journey at the same average speed and reached at City G at 6:45 p.m.

1. Find Ken'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 Rachel had travelled until Rachel overtook Ken
= 3 x 84
= 252 km

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

Ken's average speed
= 252 ÷ 6
= 42 km/h

(b)
From 10 a.m. to 6:45 p.m. = 8 h 45 min

1 h = 60 min
8 h 45 min = 8 ⁴⁵ ₆₀
 h = 8 ³₄ h

Distance between the two cities
= 8 ³₄ x 84
= ³⁵₄ x 84
= 735 km

Answer(s): (a) 42 km/h; (b) 735 km