At 2.30 p.m., Wendy and Xavier left Hotel E for Hotel F at average speeds of 96 km/h and 70 km/h respectively. Upon reaching Hotel F, Wendy rested for 25 minutes. She then headed back for Hotel E at an average speed of 96 km/h along the same route. Xavier and Wendy met each other on their way at 6 p.m.

1. How much more distance had Wendy covered than Xavier when they met on their way?
2. How far apart were Hotel E and Hotel F? Express your answer in mixed number.

(a)
Duration from 2.30 p.m. to 6 p.m. = 3 h 30 min = 3¹₂ h
Duration from 2.30 p.m. to 6 p.m. without 25 min rest = 3 h 5 min = 3¹₁₂ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
5 min = ⁵₆₀ = ¹₁₂ h


Distance covered by Wendy
= 96 x 3¹₁₂
= 96 x ³⁷₁₂ 
= 296 km

Distance covered by Xavier
= 70 x 3¹₁₂
= 70 x ³⁷₁₂
= 245 km

Distance that Wendy covered more than Xavier
= 296 - 245
= 51 km

(b)
Distance between Hotel E and Hotel F
= (296 + 245) ÷ 2
= 541 ÷ 2
= 270¹₂ km

Answer(s): (a) 51 km; (b) 270¹₂ km