At 1.30 p.m., Opal and Oliver left Hotel N for Hotel P at average speeds of 84 km/h and 66 km/h respectively. Upon reaching Hotel P, Opal rested for 10 minutes. She then headed back for Hotel N at an average speed of 84 km/h along the same route. Oliver and Opal met each other on their way at 5 p.m.

1. How much more distance had Opal covered than Oliver when they met on their way?
2. How far apart were Hotel N and Hotel P? Express your answer in mixed number.

(a)
Duration from 1.30 p.m. to 5 p.m. = 3 h 30 min = 3¹₂ h
Duration from 1.30 p.m. to 5 p.m. without 10 min rest = 3 h 20 min = 3¹₃ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
20 min = ²⁰₆₀ = ¹₃ h


Distance covered by Opal
= 84 x 3¹₃
= 84 x ¹⁰₃ 
= 280 km

Distance covered by Oliver
= 66 x 3¹₃
= 66 x ¹⁰₃
= 231 km

Distance that Opal covered more than Oliver
= 280 - 231
= 49 km

(b)
Distance between Hotel N and Hotel P
= (280 + 231) ÷ 2
= 511 ÷ 2
= 255¹₂ km

Answer(s): (a) 49 km; (b) 255¹₂ km