At 3.40 p.m., Hilda and Peter left Hotel G for Hotel H at average speeds of 90 km/h and 54 km/h respectively. Upon reaching Hotel H, Hilda rested for 10 minutes. She then headed back for Hotel G at an average speed of 90 km/h along the same route. Peter and Hilda met each other on their way at 7 p.m.

1. How much more distance had Hilda covered than Peter when they met on their way?
2. How far apart were Hotel G and Hotel H? 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 Hilda
= 90 x 3¹₆
= 90 x ¹⁹₆ 
= 285 km

Distance covered by Peter
= 54 x 3¹₆
= 54 x ¹⁹₆
= 180 km

Distance that Hilda covered more than Peter
= 285 - 180
= 105 km

(b)
Distance between Hotel G and Hotel H
= (285 + 180) ÷ 2
= 465 ÷ 2
= 232¹₂ km

Answer(s): (a) 105 km; (b) 232¹₂ km