At 9 a.m., Luis started from City B and travelled towards City C and his speed remained constant throughout. At 10 a.m., Nora started her journey from City B towards City C at an average speed of 84 km/h. Nora overtook Luis at 3 p.m. After overtaking, Nora carried on her journey at the same average speed and reached at City C at 6:25 p.m.

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

(a)
From 10 a.m. to 3 p.m. = 5 h

Distance that Nora had travelled until Nora overtook Luis
= 5 x 84
= 420 km

From 9 a.m. to 3 p.m. = 6 h

Luis's average speed
= 420 ÷ 6
= 70 km/h

(b)
From 10 a.m. to 6:25 p.m. = 8 h 25 min

1 h = 60 min
8 h 25 min = 8 ²⁵ ₆₀
 h = 8 ⁵₁₂ h

Distance between the two cities
= 8 ⁵₁₂ x 84
= ¹⁰¹₁₂ x 84
= 707 km

Answer(s): (a) 70 km/h; (b) 707 km