At 2.20 p.m., Jane and Luke left Hotel P for Hotel Q at average speeds of 66 km/h and 54 km/h respectively. Upon reaching Hotel Q, Jane rested for 10 minutes. She then headed back for Hotel P at an average speed of 66 km/h along the same route. Luke and Jane met each other on their way at 7 p.m.

1. How much more distance had Jane covered than Luke when they met on their way?
2. How far apart were Hotel P and Hotel Q? Express your answer in mixed number.

(a)
Duration from 2.20 p.m. to 7 p.m. = 4 h 40 min = 4²₃ h
Duration from 2.20 p.m. to 7 p.m. without 10 min rest = 4 h 30 min = 4¹₂ h

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


Distance covered by Jane
= 66 x 4¹₂
= 66 x ⁹₂ 
= 297 km

Distance covered by Luke
= 54 x 4¹₂
= 54 x ⁹₂
= 252 km

Distance that Jane covered more than Luke
= 297 - 252
= 45 km

(b)
Distance between Hotel P and Hotel Q
= (297 + 252) ÷ 2
= 549 ÷ 2
= 274¹₂ km

Answer(s): (a) 45 km; (b) 274¹₂ km