At 3.30 p.m., Rachel and Luis left Hotel R for Hotel S at average speeds of 72 km/h and 54 km/h respectively. Upon reaching Hotel S, Rachel rested for 15 minutes. She then headed back for Hotel R at an average speed of 72 km/h along the same route. Luis and Rachel met each other on their way at 7 p.m.

1. How much more distance had Rachel covered than Luis when they met on their way?
2. How far apart were Hotel R and Hotel S? Express your answer in mixed number.

(a)
Duration from 3.30 p.m. to 7 p.m. = 3 h 30 min = 3¹₂ h
Duration from 3.30 p.m. to 7 p.m. without 15 min rest = 3 h 15 min = 3¹₄ h

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


Distance covered by Rachel
= 72 x 3¹₄
= 72 x ¹³₄ 
= 234 km

Distance covered by Luis
= 54 x 3¹₄
= 54 x ¹³₄
= 189 km

Distance that Rachel covered more than Luis
= 234 - 189
= 45 km

(b)
Distance between Hotel R and Hotel S
= (234 + 189) ÷ 2
= 423 ÷ 2
= 211¹₂ km

Answer(s): (a) 45 km; (b) 211¹₂ km