At 5.40 p.m., Gem and Flynn left Hotel F for Hotel G at average speeds of 78 km/h and 60 km/h respectively. Upon reaching Hotel G, Gem rested for 10 minutes. She then headed back for Hotel F at an average speed of 78 km/h along the same route. Flynn and Gem met each other on their way at 9 p.m.

1. How much more distance had Gem covered than Flynn when they met on their way?
2. How far apart were Hotel F and Hotel G? Express your answer in mixed number.

(a)
Duration from 5.40 p.m. to 9 p.m. = 3 h 20 min = 3¹₃ h
Duration from 5.40 p.m. to 9 p.m. without 10 min rest = 3 h 10 min = 3¹₆ h

60 min = 1 h
20 min = ²⁰₆₀ = ¹₃ h
10 min = ¹⁰₆₀ = ¹₆ h


Distance covered by Gem
= 78 x 3¹₆
= 78 x ¹⁹₆ 
= 247 km

Distance covered by Flynn
= 60 x 3¹₆
= 60 x ¹⁹₆
= 200 km

Distance that Gem covered more than Flynn
= 247 - 200
= 47 km

(b)
Distance between Hotel F and Hotel G
= (247 + 200) ÷ 2
= 447 ÷ 2
= 223¹₂ km

Answer(s): (a) 47 km; (b) 223¹₂ km