At 2.20 p.m., Victoria and Japheth left Hotel G for Hotel H at average speeds of 82 km/h and 60 km/h respectively. Upon reaching Hotel H, Victoria rested for 10 minutes. She then headed back for Hotel G at an average speed of 82 km/h along the same route. Japheth and Victoria met each other on their way at 6 p.m.

1. How much more distance had Victoria covered than Japheth when they met on their way?
2. How far apart were Hotel G and Hotel H? Express your answer in mixed number.

(a)
Duration from 2.20 p.m. to 6 p.m. = 3 h 40 min = 3²₃ h
Duration from 2.20 p.m. to 6 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 Victoria
= 82 x 3¹₂
= 82 x ⁷₂ 
= 287 km

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

Distance that Victoria covered more than Japheth
= 287 - 220
= 67 km

(b)
Distance between Hotel G and Hotel H
= (287 + 220) ÷ 2
= 507 ÷ 2
= 253¹₂ km

Answer(s): (a) 67 km; (b) 253¹₂ km