At 1.25 p.m., Elyse and Gabriel left Hotel W for Hotel X at average speeds of 72 km/h and 60 km/h respectively. Upon reaching Hotel X, Elyse rested for 20 minutes. She then headed back for Hotel W at an average speed of 72 km/h along the same route. Gabriel and Elyse met each other on their way at 6 p.m.

1. How much more distance had Elyse covered than Gabriel when they met on their way?
2. How far apart were Hotel W and Hotel X? Express your answer in mixed number.

(a)
Duration from 1.25 p.m. to 6 p.m. = 4 h 35 min = 4⁷₁₂ h
Duration from 1.25 p.m. to 6 p.m. without 20 min rest = 4 h 15 min = 4¹₄ h

60 min = 1 h
35 min = ³⁵₆₀ = ⁷₁₂ h
15 min = ¹⁵₆₀ = ¹₄ h


Distance covered by Elyse
= 72 x 4¹₄
= 72 x ¹⁷₄ 
= 306 km

Distance covered by Gabriel
= 60 x 4¹₄
= 60 x ¹⁷₄
= 275 km

Distance that Elyse covered more than Gabriel
= 306 - 275
= 31 km

(b)
Distance between Hotel W and Hotel X
= (306 + 275) ÷ 2
= 581 ÷ 2
= 290¹₂ km

Answer(s): (a) 31 km; (b) 290¹₂ km