At 1.30 p.m., Yen and Liam left Hotel F for Hotel G at average speeds of 81 km/h and 66 km/h respectively. Upon reaching Hotel G, Yen rested for 10 minutes. She then headed back for Hotel F at an average speed of 81 km/h along the same route. Liam and Yen met each other on their way at 5 p.m.

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

(a)
Duration from 1.30 p.m. to 5 p.m. = 3 h 30 min = 3¹₂ h
Duration from 1.30 p.m. to 5 p.m. without 10 min rest = 3 h 20 min = 3¹₃ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
20 min = ²⁰₆₀ = ¹₃ h


Distance covered by Yen
= 81 x 3¹₃
= 81 x ¹⁰₃ 
= 270 km

Distance covered by Liam
= 66 x 3¹₃
= 66 x ¹⁰₃
= 231 km

Distance that Yen covered more than Liam
= 270 - 231
= 39 km

(b)
Distance between Hotel F and Hotel G
= (270 + 231) ÷ 2
= 501 ÷ 2
= 250¹₂ km

Answer(s): (a) 39 km; (b) 250¹₂ km