At 4.20 p.m., Rachel and Pierre left Hotel U for Hotel V at average speeds of 70 km/h and 60 km/h respectively. Upon reaching Hotel V, Rachel rested for 10 minutes. She then headed back for Hotel U at an average speed of 70 km/h along the same route. Pierre and Rachel met each other on their way at 8 p.m.

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

(a)
Duration from 4.20 p.m. to 8 p.m. = 3 h 40 min = 3²₃ h
Duration from 4.20 p.m. to 8 p.m. without 10 min rest = 3 h 30 min = 3¹₂ h

60 min = 1 h
40 min = ⁴⁰₆₀ = ²₃ h
30 min = ³⁰₆₀ = ¹₂ h


Distance covered by Rachel
= 70 x 3¹₂
= 70 x ⁷₂ 
= 245 km

Distance covered by Pierre
= 60 x 3¹₂
= 60 x ⁷₂
= 220 km

Distance that Rachel covered more than Pierre
= 245 - 220
= 25 km

(b)
Distance between Hotel U and Hotel V
= (245 + 220) ÷ 2
= 465 ÷ 2
= 232¹₂ km

Answer(s): (a) 25 km; (b) 232¹₂ km