At 4.30 p.m., Gem and Rael left Hotel X for Hotel Y at average speeds of 84 km/h and 54 km/h respectively. Upon reaching Hotel Y, Gem rested for 20 minutes. She then headed back for Hotel X at an average speed of 84 km/h along the same route. Rael and Gem met each other on their way at 8 p.m.

1. How much more distance had Gem covered than Rael when they met on their way?
2. How far apart were Hotel X and Hotel Y? 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 20 min rest = 3 h 10 min = 3¹₆ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
10 min = ¹⁰₆₀ = ¹₆ h


Distance covered by Gem
= 84 x 3¹₆
= 84 x ¹⁹₆ 
= 266 km

Distance covered by Rael
= 54 x 3¹₆
= 54 x ¹⁹₆
= 189 km

Distance that Gem covered more than Rael
= 266 - 189
= 77 km

(b)
Distance between Hotel X and Hotel Y
= (266 + 189) ÷ 2
= 455 ÷ 2
= 227¹₂ km

Answer(s): (a) 77 km; (b) 227¹₂ km