At 4.30 p.m., Fanny and Ethan left Hotel G for Hotel H at average speeds of 99 km/h and 54 km/h respectively. Upon reaching Hotel H, Fanny rested for 10 minutes. She then headed back for Hotel G at an average speed of 99 km/h along the same route. Ethan and Fanny met each other on their way at 8 p.m.

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

Distance covered by Ethan
= 54 x 3¹₃
= 54 x ¹⁰₃
= 189 km

Distance that Fanny covered more than Ethan
= 330 - 189
= 141 km

(b)
Distance between Hotel G and Hotel H
= (330 + 189) ÷ 2
= 519 ÷ 2
= 259¹₂ km

Answer(s): (a) 141 km; (b) 259¹₂ km