At 5.30 p.m., Shannon and Tom left Hotel J for Hotel K at average speeds of 78 km/h and 50 km/h respectively. Upon reaching Hotel K, Shannon rested for 10 minutes. She then headed back for Hotel J at an average speed of 78 km/h along the same route. Tom and Shannon met each other on their way at 9 p.m.

1. How much more distance had Shannon covered than Tom when they met on their way?
2. How far apart were Hotel J and Hotel K? Express your answer in mixed number.

(a)
Duration from 5.30 p.m. to 9 p.m. = 3 h 30 min = 3¹₂ h
Duration from 5.30 p.m. to 9 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 Shannon
= 78 x 3¹₃
= 78 x ¹⁰₃ 
= 260 km

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

Distance that Shannon covered more than Tom
= 260 - 175
= 85 km

(b)
Distance between Hotel J and Hotel K
= (260 + 175) ÷ 2
= 435 ÷ 2
= 217¹₂ km

Answer(s): (a) 85 km; (b) 217¹₂ km