At 2.30 p.m., Jean and Elijah left Hotel P for Hotel Q at average speeds of 84 km/h and 54 km/h respectively. Upon reaching Hotel Q, Jean rested for 20 minutes. She then headed back for Hotel P at an average speed of 84 km/h along the same route. Elijah and Jean met each other on their way at 7 p.m.

1. How much more distance had Jean covered than Elijah 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 2.30 p.m. to 7 p.m. = 4 h 30 min = 4¹₂ h
Duration from 2.30 p.m. to 7 p.m. without 20 min rest = 4 h 10 min = 4¹₆ h

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


Distance covered by Jean
= 84 x 4¹₆
= 84 x ²⁵₆ 
= 350 km

Distance covered by Elijah
= 54 x 4¹₆
= 54 x ²⁵₆
= 243 km

Distance that Jean covered more than Elijah
= 350 - 243
= 107 km

(b)
Distance between Hotel P and Hotel Q
= (350 + 243) ÷ 2
= 593 ÷ 2
= 296¹₂ km

Answer(s): (a) 107 km; (b) 296¹₂ km