At 4.30 p.m., Marion and Billy left Hotel S for Hotel T at average speeds of 96 km/h and 58 km/h respectively. Upon reaching Hotel T, Marion rested for 25 minutes. She then headed back for Hotel S at an average speed of 96 km/h along the same route. Billy and Marion met each other on their way at 8 p.m.

1. How much more distance had Marion covered than Billy when they met on their way?
2. How far apart were Hotel S and Hotel T? 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 25 min rest = 3 h 5 min = 3¹₁₂ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
5 min = ⁵₆₀ = ¹₁₂ h


Distance covered by Marion
= 96 x 3¹₁₂
= 96 x ³⁷₁₂ 
= 296 km

Distance covered by Billy
= 58 x 3¹₁₂
= 58 x ³⁷₁₂
= 203 km

Distance that Marion covered more than Billy
= 296 - 203
= 93 km

(b)
Distance between Hotel S and Hotel T
= (296 + 203) ÷ 2
= 499 ÷ 2
= 249¹₂ km

Answer(s): (a) 93 km; (b) 249¹₂ km