At 4.30 p.m., Zoe and Bobby left Hotel F for Hotel G at average speeds of 68 km/h and 56 km/h respectively. Upon reaching Hotel G, Zoe rested for 15 minutes. She then headed back for Hotel F at an average speed of 68 km/h along the same route. Bobby and Zoe met each other on their way at 9 p.m.

1. How much more distance had Zoe covered than Bobby 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 9 p.m. = 4 h 30 min = 4¹₂ h
Duration from 4.30 p.m. to 9 p.m. without 15 min rest = 4 h 15 min = 4¹₄ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
15 min = ¹⁵₆₀ = ¹₄ h


Distance covered by Zoe
= 68 x 4¹₄
= 68 x ¹⁷₄ 
= 289 km

Distance covered by Bobby
= 56 x 4¹₄
= 56 x ¹⁷₄
= 252 km

Distance that Zoe covered more than Bobby
= 289 - 252
= 37 km

(b)
Distance between Hotel F and Hotel G
= (289 + 252) ÷ 2
= 541 ÷ 2
= 270¹₂ km

Answer(s): (a) 37 km; (b) 270¹₂ km