At 5.20 p.m., Jade and Japheth left Hotel H for Hotel J at average speeds of 90 km/h and 60 km/h respectively. Upon reaching Hotel J, Jade rested for 10 minutes. She then headed back for Hotel H at an average speed of 90 km/h along the same route. Japheth and Jade met each other on their way at 9 p.m.

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

(a)
Duration from 5.20 p.m. to 9 p.m. = 3 h 40 min = 3²₃ h
Duration from 5.20 p.m. to 9 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 Jade
= 90 x 3¹₂
= 90 x ⁷₂ 
= 315 km

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

Distance that Jade covered more than Japheth
= 315 - 220
= 95 km

(b)
Distance between Hotel H and Hotel J
= (315 + 220) ÷ 2
= 535 ÷ 2
= 267¹₂ km

Answer(s): (a) 95 km; (b) 267¹₂ km