At 3.40 p.m., Yen and Elijah left Hotel X for Hotel Y at average speeds of 78 km/h and 60 km/h respectively. Upon reaching Hotel Y, Yen rested for 10 minutes. She then headed back for Hotel X at an average speed of 78 km/h along the same route. Elijah and Yen met each other on their way at 7 p.m.

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

(a)
Duration from 3.40 p.m. to 7 p.m. = 3 h 20 min = 3¹₃ h
Duration from 3.40 p.m. to 7 p.m. without 10 min rest = 3 h 10 min = 3¹₆ h

60 min = 1 h
20 min = ²⁰₆₀ = ¹₃ h
10 min = ¹⁰₆₀ = ¹₆ h


Distance covered by Yen
= 78 x 3¹₆
= 78 x ¹⁹₆ 
= 247 km

Distance covered by Elijah
= 60 x 3¹₆
= 60 x ¹⁹₆
= 200 km

Distance that Yen covered more than Elijah
= 247 - 200
= 47 km

(b)
Distance between Hotel X and Hotel Y
= (247 + 200) ÷ 2
= 447 ÷ 2
= 223¹₂ km

Answer(s): (a) 47 km; (b) 223¹₂ km