At 4.35 p.m., Kimberly and Gabriel left Hotel W for Hotel X at average speeds of 72 km/h and 60 km/h respectively. Upon reaching Hotel X, Kimberly rested for 15 minutes. She then headed back for Hotel W at an average speed of 72 km/h along the same route. Gabriel and Kimberly met each other on their way at 8 p.m.

1. How much more distance had Kimberly covered than Gabriel when they met on their way?
2. How far apart were Hotel W and Hotel X? Express your answer in mixed number.

(a)
Duration from 4.35 p.m. to 8 p.m. = 3 h 25 min = 3⁵₁₂ h
Duration from 4.35 p.m. to 8 p.m. without 15 min rest = 3 h 10 min = 3¹₆ h

60 min = 1 h
25 min = ²⁵₆₀ = ⁵₁₂ h
10 min = ¹⁰₆₀ = ¹₆ h


Distance covered by Kimberly
= 72 x 3¹₆
= 72 x ¹⁹₆ 
= 228 km

Distance covered by Gabriel
= 60 x 3¹₆
= 60 x ¹⁹₆
= 205 km

Distance that Kimberly covered more than Gabriel
= 228 - 205
= 23 km

(b)
Distance between Hotel W and Hotel X
= (228 + 205) ÷ 2
= 433 ÷ 2
= 216¹₂ km

Answer(s): (a) 23 km; (b) 216¹₂ km