At 4.30 p.m., Zoe and Vaidev left Hotel L for Hotel M at average speeds of 80 km/h and 62 km/h respectively. Upon reaching Hotel M, Zoe rested for 15 minutes. She then headed back for Hotel L at an average speed of 80 km/h along the same route. Vaidev and Zoe met each other on their way at 8 p.m.

1. How much more distance had Zoe covered than Vaidev when they met on their way?
2. How far apart were Hotel L and Hotel M? Express your answer in mixed number.

(a)
Duration from 4.30 p.m. to 8 p.m. = 3 h 30 min = 3¹₂ h
Duration from 4.30 p.m. to 8 p.m. without 15 min rest = 3 h 15 min = 3¹₄ h

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


Distance covered by Zoe
= 80 x 3¹₄
= 80 x ¹³₄ 
= 260 km

Distance covered by Vaidev
= 62 x 3¹₄
= 62 x ¹³₄
= 217 km

Distance that Zoe covered more than Vaidev
= 260 - 217
= 43 km

(b)
Distance between Hotel L and Hotel M
= (260 + 217) ÷ 2
= 477 ÷ 2
= 238¹₂ km

Answer(s): (a) 43 km; (b) 238¹₂ km