At 8 a.m., Pierre started from City R and travelled towards City S and his speed remained constant throughout. At 9 a.m., Usha started her journey from City R towards City S at an average speed of 84 km/h. Usha overtook Pierre at 2 p.m. After overtaking, Usha carried on her journey at the same average speed and reached at City S at 6:45 p.m.

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

(a)
From 9 a.m. to 2 p.m. = 5 h

Distance that Usha had travelled until Usha overtook Pierre
= 5 x 84
= 420 km

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

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

(b)
From 9 a.m. to 6:45 p.m. = 9 h 45 min

1 h = 60 min
9 h 45 min = 9 ⁴⁵ ₆₀
 h = 9 ³₄ h

Distance between the two cities
= 9 ³₄ x 84
= ³⁹₄ x 84
= 819 km

Answer(s): (a) 70 km/h; (b) 819 km