At 4.30 p.m., Zara and Glen left Hotel F for Hotel G at average speeds of 72 km/h and 54 km/h respectively. Upon reaching Hotel G, Zara rested for 10 minutes. She then headed back for Hotel F at an average speed of 72 km/h along the same route. Glen and Zara met each other on their way at 8 p.m.

1. How much more distance had Zara covered than Glen 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 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 Zara
= 72 x 3¹₃
= 72 x ¹⁰₃ 
= 240 km

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

Distance that Zara covered more than Glen
= 240 - 189
= 51 km

(b)
Distance between Hotel F and Hotel G
= (240 + 189) ÷ 2
= 429 ÷ 2
= 214¹₂ km

Answer(s): (a) 51 km; (b) 214¹₂ km