At 8 a.m., Peter started from City N and travelled towards City P and his speed remained constant throughout. At 9 a.m., Tiffany started her journey from City N towards City P at an average speed of 78 km/h. Tiffany overtook Peter at 2 p.m. After overtaking, Tiffany carried on her journey at the same average speed and reached at City P at 3:30 p.m.

1. Find Peter'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 Tiffany had travelled until Tiffany overtook Peter
= 5 x 78
= 390 km

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

Peter's average speed
= 390 ÷ 6
= 65 km/h

(b)
From 9 a.m. to 3:30 p.m. = 6 h 30 min

1 h = 60 min
6 h 30 min = 6 ³⁰ ₆₀
 h = 6 ¹₂ h

Distance between the two cities
= 6 ¹₂ x 78
= ¹³₂ x 78
= 507 km

Answer(s): (a) 65 km/h; (b) 507 km