At 3.20 p.m., Zoe and Albert left Hotel X for Hotel Y at average speeds of 90 km/h and 66 km/h respectively. Upon reaching Hotel Y, Zoe rested for 10 minutes. She then headed back for Hotel X at an average speed of 90 km/h along the same route. Albert and Zoe met each other on their way at 7 p.m.

1. How much more distance had Zoe covered than Albert 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 3.20 p.m. to 7 p.m. = 3 h 40 min = 3²₃ h
Duration from 3.20 p.m. to 7 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 Zoe
= 90 x 3¹₂
= 90 x ⁷₂ 
= 315 km

Distance covered by Albert
= 66 x 3¹₂
= 66 x ⁷₂
= 242 km

Distance that Zoe covered more than Albert
= 315 - 242
= 73 km

(b)
Distance between Hotel X and Hotel Y
= (315 + 242) ÷ 2
= 557 ÷ 2
= 278¹₂ km

Answer(s): (a) 73 km; (b) 278¹₂ km