At 4.30 p.m., Sarah and Neave left Hotel V for Hotel W at average speeds of 84 km/h and 68 km/h respectively. Upon reaching Hotel W, Sarah rested for 15 minutes. She then headed back for Hotel V at an average speed of 84 km/h along the same route. Neave and Sarah met each other on their way at 8 p.m.

1. How much more distance had Sarah covered than Neave when they met on their way?
2. How far apart were Hotel V and Hotel W? 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 Sarah
= 84 x 3¹₄
= 84 x ¹³₄ 
= 273 km

Distance covered by Neave
= 68 x 3¹₄
= 68 x ¹³₄
= 238 km

Distance that Sarah covered more than Neave
= 273 - 238
= 35 km

(b)
Distance between Hotel V and Hotel W
= (273 + 238) ÷ 2
= 511 ÷ 2
= 255¹₂ km

Answer(s): (a) 35 km; (b) 255¹₂ km