At 2.40 p.m., Nicole and Elijah left Hotel L for Hotel M at average speeds of 84 km/h and 69 km/h respectively. Upon reaching Hotel M, Nicole rested for 15 minutes. She then headed back for Hotel L at an average speed of 84 km/h along the same route. Elijah and Nicole met each other on their way at 6 p.m.

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

(a)
Duration from 2.40 p.m. to 6 p.m. = 3 h 20 min = 3¹₃ h
Duration from 2.40 p.m. to 6 p.m. without 15 min rest = 3 h 5 min = 3¹₁₂ h

60 min = 1 h
20 min = ²⁰₆₀ = ¹₃ h
5 min = ⁵₆₀ = ¹₁₂ h


Distance covered by Nicole
= 84 x 3¹₁₂
= 84 x ³⁷₁₂ 
= 259 km

Distance covered by Elijah
= 69 x 3¹₁₂
= 69 x ³⁷₁₂
= 230 km

Distance that Nicole covered more than Elijah
= 259 - 230
= 29 km

(b)
Distance between Hotel L and Hotel M
= (259 + 230) ÷ 2
= 489 ÷ 2
= 244¹₂ km

Answer(s): (a) 29 km; (b) 244¹₂ km