At 5.20 p.m., Natalie and Elijah left Hotel H for Hotel J at average speeds of 68 km/h and 51 km/h respectively. Upon reaching Hotel J, Natalie rested for 10 minutes. She then headed back for Hotel H at an average speed of 68 km/h along the same route. Elijah and Natalie met each other on their way at 9 p.m.

1. How much more distance had Natalie covered than Elijah 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 5.20 p.m. to 9 p.m. = 3 h 40 min = 3²₃ h
Duration from 5.20 p.m. to 9 p.m. without 10 min rest = 3 h 30 min = 3¹₂ h

60 min = 1 h
40 min = ⁴⁰₆₀ = ²₃ h
30 min = ³⁰₆₀ = ¹₂ h


Distance covered by Natalie
= 68 x 3¹₂
= 68 x ⁷₂ 
= 238 km

Distance covered by Elijah
= 51 x 3¹₂
= 51 x ⁷₂
= 187 km

Distance that Natalie covered more than Elijah
= 238 - 187
= 51 km

(b)
Distance between Hotel H and Hotel J
= (238 + 187) ÷ 2
= 425 ÷ 2
= 212¹₂ km

Answer(s): (a) 51 km; (b) 212¹₂ km