At 5.30 p.m., Eva and Charlie left Hotel D for Hotel E at average speeds of 93 km/h and 66 km/h respectively. Upon reaching Hotel E, Eva rested for 10 minutes. She then headed back for Hotel D at an average speed of 93 km/h along the same route. Charlie and Eva met each other on their way at 9 p.m.

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

(a)
Duration from 5.30 p.m. to 9 p.m. = 3 h 30 min = 3¹₂ h
Duration from 5.30 p.m. to 9 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 Eva
= 93 x 3¹₃
= 93 x ¹⁰₃ 
= 310 km

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

Distance that Eva covered more than Charlie
= 310 - 231
= 79 km

(b)
Distance between Hotel D and Hotel E
= (310 + 231) ÷ 2
= 541 ÷ 2
= 270¹₂ km

Answer(s): (a) 79 km; (b) 270¹₂ km