At 1.30 p.m., Rachel and Eric left Hotel W for Hotel X at average speeds of 90 km/h and 68 km/h respectively. Upon reaching Hotel X, Rachel rested for 20 minutes. She then headed back for Hotel W at an average speed of 90 km/h along the same route. Eric and Rachel met each other on their way at 5 p.m.

1. How much more distance had Rachel covered than Eric 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 1.30 p.m. to 5 p.m. = 3 h 30 min = 3¹₂ h
Duration from 1.30 p.m. to 5 p.m. without 20 min rest = 3 h 10 min = 3¹₆ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
10 min = ¹⁰₆₀ = ¹₆ h


Distance covered by Rachel
= 90 x 3¹₆
= 90 x ¹⁹₆ 
= 285 km

Distance covered by Eric
= 68 x 3¹₆
= 68 x ¹⁹₆
= 238 km

Distance that Rachel covered more than Eric
= 285 - 238
= 47 km

(b)
Distance between Hotel W and Hotel X
= (285 + 238) ÷ 2
= 523 ÷ 2
= 261¹₂ km

Answer(s): (a) 47 km; (b) 261¹₂ km