At 5.30 p.m., Shiyun and Ahmad left Hotel Z for Hotel A at average speeds of 76 km/h and 56 km/h respectively. Upon reaching Hotel A, Shiyun rested for 15 minutes. She then headed back for Hotel Z at an average speed of 76 km/h along the same route. Ahmad and Shiyun met each other on their way at 10 p.m.

1. How much more distance had Shiyun covered than Ahmad when they met on their way?
2. How far apart were Hotel Z and Hotel A? Express your answer in mixed number.

(a)
Duration from 5.30 p.m. to 10 p.m. = 4 h 30 min = 4¹₂ h
Duration from 5.30 p.m. to 10 p.m. without 15 min rest = 4 h 15 min = 4¹₄ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
15 min = ¹⁵₆₀ = ¹₄ h


Distance covered by Shiyun
= 76 x 4¹₄
= 76 x ¹⁷₄ 
= 323 km

Distance covered by Ahmad
= 56 x 4¹₄
= 56 x ¹⁷₄
= 252 km

Distance that Shiyun covered more than Ahmad
= 323 - 252
= 71 km

(b)
Distance between Hotel Z and Hotel A
= (323 + 252) ÷ 2
= 575 ÷ 2
= 287¹₂ km

Answer(s): (a) 71 km; (b) 287¹₂ km