At 3.30 p.m., Esther and Nick left Hotel K for Hotel L at average speeds of 72 km/h and 62 km/h respectively. Upon reaching Hotel L, Esther rested for 10 minutes. She then headed back for Hotel K at an average speed of 72 km/h along the same route. Nick and Esther met each other on their way at 7 p.m.

1. How much more distance had Esther covered than Nick when they met on their way?
2. How far apart were Hotel K and Hotel L? 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 Esther
= 72 x 3¹₃
= 72 x ¹⁰₃ 
= 240 km

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

Distance that Esther covered more than Nick
= 240 - 217
= 23 km

(b)
Distance between Hotel K and Hotel L
= (240 + 217) ÷ 2
= 457 ÷ 2
= 228¹₂ km

Answer(s): (a) 23 km; (b) 228¹₂ km