At 3.15 p.m., Marion and Justin left Hotel V for Hotel W at average speeds of 84 km/h and 64 km/h respectively. Upon reaching Hotel W, Marion rested for 10 minutes. She then headed back for Hotel V at an average speed of 84 km/h along the same route. Justin and Marion met each other on their way at 7 p.m.

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

(a)
Duration from 3.15 p.m. to 7 p.m. = 3 h 45 min = 3³₄ h
Duration from 3.15 p.m. to 7 p.m. without 10 min rest = 3 h 35 min = 3⁷₁₂ h

60 min = 1 h
45 min = ⁴⁵₆₀ = ³₄ h
35 min = ³⁵₆₀ = ⁷₁₂ h


Distance covered by Marion
= 84 x 3⁷₁₂
= 84 x ⁴³₁₂ 
= 301 km

Distance covered by Justin
= 64 x 3⁷₁₂
= 64 x ⁴³₁₂
= 240 km

Distance that Marion covered more than Justin
= 301 - 240
= 61 km

(b)
Distance between Hotel V and Hotel W
= (301 + 240) ÷ 2
= 541 ÷ 2
= 270¹₂ km

Answer(s): (a) 61 km; (b) 270¹₂ km