At 5.30 p.m., Elyse and Ethan left Hotel Q for Hotel R at average speeds of 99 km/h and 62 km/h respectively. Upon reaching Hotel R, Elyse rested for 10 minutes. She then headed back for Hotel Q at an average speed of 99 km/h along the same route. Ethan and Elyse met each other on their way at 9 p.m.

1. How much more distance had Elyse covered than Ethan when they met on their way?
2. How far apart were Hotel Q and Hotel R? 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 Elyse
= 99 x 3¹₃
= 99 x ¹⁰₃ 
= 330 km

Distance covered by Ethan
= 62 x 3¹₃
= 62 x ¹⁰₃
= 217 km

Distance that Elyse covered more than Ethan
= 330 - 217
= 113 km

(b)
Distance between Hotel Q and Hotel R
= (330 + 217) ÷ 2
= 547 ÷ 2
= 273¹₂ km

Answer(s): (a) 113 km; (b) 273¹₂ km