At 1.30 p.m., Betty and Cody left Hotel L for Hotel M at average speeds of 81 km/h and 58 km/h respectively. Upon reaching Hotel M, Betty rested for 10 minutes. She then headed back for Hotel L at an average speed of 81 km/h along the same route. Cody and Betty met each other on their way at 5 p.m.

1. How much more distance had Betty covered than Cody 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 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 10 min rest = 3 h 20 min = 3¹₃ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
20 min = ²⁰₆₀ = ¹₃ h


Distance covered by Betty
= 81 x 3¹₃
= 81 x ¹⁰₃ 
= 270 km

Distance covered by Cody
= 58 x 3¹₃
= 58 x ¹⁰₃
= 203 km

Distance that Betty covered more than Cody
= 270 - 203
= 67 km

(b)
Distance between Hotel L and Hotel M
= (270 + 203) ÷ 2
= 473 ÷ 2
= 236¹₂ km

Answer(s): (a) 67 km; (b) 236¹₂ km