At 1.30 p.m., Shiyun and Riordan left Hotel R for Hotel S at average speeds of 84 km/h and 62 km/h respectively. Upon reaching Hotel S, Shiyun rested for 10 minutes. She then headed back for Hotel R at an average speed of 84 km/h along the same route. Riordan and Shiyun met each other on their way at 5 p.m.

1. How much more distance had Shiyun covered than Riordan when they met on their way?
2. How far apart were Hotel R and Hotel S? 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 Shiyun
= 84 x 3¹₃
= 84 x ¹⁰₃ 
= 280 km

Distance covered by Riordan
= 62 x 3¹₃
= 62 x ¹⁰₃
= 217 km

Distance that Shiyun covered more than Riordan
= 280 - 217
= 63 km

(b)
Distance between Hotel R and Hotel S
= (280 + 217) ÷ 2
= 497 ÷ 2
= 248¹₂ km

Answer(s): (a) 63 km; (b) 248¹₂ km