At 3.25 p.m., Irene and Oscar left Hotel P for Hotel Q at average speeds of 81 km/h and 60 km/h respectively. Upon reaching Hotel Q, Irene rested for 15 minutes. She then headed back for Hotel P at an average speed of 81 km/h along the same route. Oscar and Irene met each other on their way at 7 p.m.

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

(a)
Duration from 3.25 p.m. to 7 p.m. = 3 h 35 min = 3⁷₁₂ h
Duration from 3.25 p.m. to 7 p.m. without 15 min rest = 3 h 20 min = 3¹₃ h

60 min = 1 h
35 min = ³⁵₆₀ = ⁷₁₂ h
20 min = ²⁰₆₀ = ¹₃ h


Distance covered by Irene
= 81 x 3¹₃
= 81 x ¹⁰₃ 
= 270 km

Distance covered by Oscar
= 60 x 3¹₃
= 60 x ¹⁰₃
= 215 km

Distance that Irene covered more than Oscar
= 270 - 215
= 55 km

(b)
Distance between Hotel P and Hotel Q
= (270 + 215) ÷ 2
= 485 ÷ 2
= 242¹₂ km

Answer(s): (a) 55 km; (b) 242¹₂ km