At 4.40 p.m., Lucy and Sam left Hotel H for Hotel J at average speeds of 84 km/h and 57 km/h respectively. Upon reaching Hotel J, Lucy rested for 10 minutes. She then headed back for Hotel H at an average speed of 84 km/h along the same route. Sam and Lucy met each other on their way at 9 p.m.

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

(a)
Duration from 4.40 p.m. to 9 p.m. = 4 h 20 min = 4¹₃ h
Duration from 4.40 p.m. to 9 p.m. without 10 min rest = 4 h 10 min = 4¹₆ h

60 min = 1 h
20 min = ²⁰₆₀ = ¹₃ h
10 min = ¹⁰₆₀ = ¹₆ h


Distance covered by Lucy
= 84 x 4¹₆
= 84 x ²⁵₆ 
= 350 km

Distance covered by Sam
= 57 x 4¹₆
= 57 x ²⁵₆
= 247 km

Distance that Lucy covered more than Sam
= 350 - 247
= 103 km

(b)
Distance between Hotel H and Hotel J
= (350 + 247) ÷ 2
= 597 ÷ 2
= 298¹₂ km

Answer(s): (a) 103 km; (b) 298¹₂ km