At 9 a.m., Luis started from City R and travelled towards City S and his speed remained constant throughout. At 10 a.m., Esther started her journey from City R towards City S at an average speed of 84 km/h. Esther overtook Luis at 3 p.m. After overtaking, Esther carried on her journey at the same average speed and reached at City S at 5:20 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 Esther had travelled until Esther 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 5:20 p.m. = 7 h 20 min

1 h = 60 min
7 h 20 min = 7 ²⁰ ₆₀
 h = 7 ¹₃ h

Distance between the two cities
= 7 ¹₃ x 84
= ²²₃ x 84
= 616 km

Answer(s): (a) 70 km/h; (b) 616 km