At 2.30 p.m., Gabby and Cole left Hotel R for Hotel S at average speeds of 72 km/h and 50 km/h respectively. Upon reaching Hotel S, Gabby rested for 10 minutes. She then headed back for Hotel R at an average speed of 72 km/h along the same route. Cole and Gabby met each other on their way at 6 p.m.

1. How much more distance had Gabby covered than Cole when they met on their way?
2. How far apart were Hotel R and Hotel S? Express your answer in mixed number.

(a)
Duration from 2.30 p.m. to 6 p.m. = 3 h 30 min = 3¹₂ h
Duration from 2.30 p.m. to 6 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 Gabby
= 72 x 3¹₃
= 72 x ¹⁰₃ 
= 240 km

Distance covered by Cole
= 50 x 3¹₃
= 50 x ¹⁰₃
= 175 km

Distance that Gabby covered more than Cole
= 240 - 175
= 65 km

(b)
Distance between Hotel R and Hotel S
= (240 + 175) ÷ 2
= 415 ÷ 2
= 207¹₂ km

Answer(s): (a) 65 km; (b) 207¹₂ km