At 5.30 p.m., Elyse and Warren left Hotel P for Hotel Q at average speeds of 72 km/h and 50 km/h respectively. Upon reaching Hotel Q, Elyse rested for 20 minutes. She then headed back for Hotel P at an average speed of 72 km/h along the same route. Warren and Elyse met each other on their way at 9 p.m.

1. How much more distance had Elyse covered than Warren when they met on their way?
2. How far apart were Hotel P and Hotel Q? Express your answer in mixed number.

(a)
Duration from 5.30 p.m. to 9 p.m. = 3 h 30 min = 3¹₂ h
Duration from 5.30 p.m. to 9 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 Elyse
= 72 x 3¹₆
= 72 x ¹⁹₆ 
= 228 km

Distance covered by Warren
= 50 x 3¹₆
= 50 x ¹⁹₆
= 175 km

Distance that Elyse covered more than Warren
= 228 - 175
= 53 km

(b)
Distance between Hotel P and Hotel Q
= (228 + 175) ÷ 2
= 403 ÷ 2
= 201¹₂ km

Answer(s): (a) 53 km; (b) 201¹₂ km