At 8 a.m., Ken started from City Z and travelled towards City A and his speed remained constant throughout. At 10 a.m., Barbara started her journey from City Z towards City A at an average speed of 87 km/h. Barbara overtook Ken at 2 p.m. After overtaking, Barbara carried on her journey at the same average speed and reached at City A at 2:20 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 2 p.m. = 4 h

Distance that Barbara had travelled until Barbara overtook Ken
= 4 x 87
= 348 km

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

Ken's average speed
= 348 ÷ 6
= 58 km/h

(b)
From 10 a.m. to 2:20 p.m. = 4 h 20 min

1 h = 60 min
4 h 20 min = 4 ²⁰ ₆₀
 h = 4 ¹₃ h

Distance between the two cities
= 4 ¹₃ x 87
= ¹³₃ x 87
= 377 km

Answer(s): (a) 58 km/h; (b) 377 km