At 7 a.m., Riordan started from City M and travelled towards City N and his speed remained constant throughout. At 9 a.m., Esther started her journey from City M towards City N at an average speed of 78 km/h. Esther overtook Riordan at 1 p.m. After overtaking, Esther carried on her journey at the same average speed and reached at City N at 6:40 p.m.

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

(a)
From 9 a.m. to 1 p.m. = 4 h

Distance that Esther had travelled until Esther overtook Riordan
= 4 x 78
= 312 km

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

Riordan's average speed
= 312 ÷ 6
= 52 km/h

(b)
From 9 a.m. to 6:40 p.m. = 9 h 40 min

1 h = 60 min
9 h 40 min = 9 ⁴⁰ ₆₀
 h = 9 ²₃ h

Distance between the two cities
= 9 ²₃ x 78
= ²⁹₃ x 78
= 754 km

Answer(s): (a) 52 km/h; (b) 754 km