At 1.20 p.m., Olivia and Vincent left Hotel X for Hotel Y at average speeds of 72 km/h and 51 km/h respectively. Upon reaching Hotel Y, Olivia rested for 10 minutes. She then headed back for Hotel X at an average speed of 72 km/h along the same route. Vincent and Olivia met each other on their way at 5 p.m.

1. How much more distance had Olivia covered than Vincent when they met on their way?
2. How far apart were Hotel X and Hotel Y? Express your answer in mixed number.

(a)
Duration from 1.20 p.m. to 5 p.m. = 3 h 40 min = 3²₃ h
Duration from 1.20 p.m. to 5 p.m. without 10 min rest = 3 h 30 min = 3¹₂ h

60 min = 1 h
40 min = ⁴⁰₆₀ = ²₃ h
30 min = ³⁰₆₀ = ¹₂ h


Distance covered by Olivia
= 72 x 3¹₂
= 72 x ⁷₂ 
= 252 km

Distance covered by Vincent
= 51 x 3¹₂
= 51 x ⁷₂
= 187 km

Distance that Olivia covered more than Vincent
= 252 - 187
= 65 km

(b)
Distance between Hotel X and Hotel Y
= (252 + 187) ÷ 2
= 439 ÷ 2
= 219¹₂ km

Answer(s): (a) 65 km; (b) 219¹₂ km