At 4.30 p.m., Ivory and Rael left Hotel C for Hotel D at average speeds of 96 km/h and 66 km/h respectively. Upon reaching Hotel D, Ivory rested for 10 minutes. She then headed back for Hotel C at an average speed of 96 km/h along the same route. Rael and Ivory met each other on their way at 8 p.m.

1. How much more distance had Ivory covered than Rael when they met on their way?
2. How far apart were Hotel C and Hotel D? Express your answer in mixed number.

(a)
Duration from 4.30 p.m. to 8 p.m. = 3 h 30 min = 3¹₂ h
Duration from 4.30 p.m. to 8 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 Ivory
= 96 x 3¹₃
= 96 x ¹⁰₃ 
= 320 km

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

Distance that Ivory covered more than Rael
= 320 - 231
= 89 km

(b)
Distance between Hotel C and Hotel D
= (320 + 231) ÷ 2
= 551 ÷ 2
= 275¹₂ km

Answer(s): (a) 89 km; (b) 275¹₂ km