At 5.20 p.m., Zoe and Asher left Hotel T for Hotel U at average speeds of 84 km/h and 69 km/h respectively. Upon reaching Hotel U, Zoe rested for 10 minutes. She then headed back for Hotel T at an average speed of 84 km/h along the same route. Asher and Zoe met each other on their way at 9 p.m.

1. How much more distance had Zoe covered than Asher when they met on their way?
2. How far apart were Hotel T and Hotel U? 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 Zoe
= 84 x 3¹₂
= 84 x ⁷₂ 
= 294 km

Distance covered by Asher
= 69 x 3¹₂
= 69 x ⁷₂
= 253 km

Distance that Zoe covered more than Asher
= 294 - 253
= 41 km

(b)
Distance between Hotel T and Hotel U
= (294 + 253) ÷ 2
= 547 ÷ 2
= 273¹₂ km

Answer(s): (a) 41 km; (b) 273¹₂ km