At 7 a.m., Ivan started from City N and travelled towards City P and his speed remained constant throughout. At 8 a.m., Marion started her journey from City N towards City P at an average speed of 66 km/h. Marion overtook Ivan at 1 p.m. After overtaking, Marion carried on her journey at the same average speed and reached at City P at 5:40 p.m.

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

(a)
From 8 a.m. to 1 p.m. = 5 h

Distance that Marion had travelled until Marion overtook Ivan
= 5 x 66
= 330 km

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

Ivan's average speed
= 330 ÷ 6
= 55 km/h

(b)
From 8 a.m. to 5:40 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 66
= ²⁹₃ x 66
= 638 km

Answer(s): (a) 55 km/h; (b) 638 km