At 3.30 p.m., Anna and Ethan left Hotel J for Hotel K at average speeds of 75 km/h and 62 km/h respectively. Upon reaching Hotel K, Anna rested for 10 minutes. She then headed back for Hotel J at an average speed of 75 km/h along the same route. Ethan and Anna met each other on their way at 7 p.m.

1. How much more distance had Anna covered than Ethan 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 3.30 p.m. to 7 p.m. = 3 h 30 min = 3¹₂ h
Duration from 3.30 p.m. to 7 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 Anna
= 75 x 3¹₃
= 75 x ¹⁰₃ 
= 250 km

Distance covered by Ethan
= 62 x 3¹₃
= 62 x ¹⁰₃
= 217 km

Distance that Anna covered more than Ethan
= 250 - 217
= 33 km

(b)
Distance between Hotel J and Hotel K
= (250 + 217) ÷ 2
= 467 ÷ 2
= 233¹₂ km

Answer(s): (a) 33 km; (b) 233¹₂ km