At 4.20 p.m., Hazel and Seth left Hotel K for Hotel L at average speeds of 80 km/h and 69 km/h respectively. Upon reaching Hotel L, Hazel rested for 10 minutes. She then headed back for Hotel K at an average speed of 80 km/h along the same route. Seth and Hazel met each other on their way at 8 p.m.

1. How much more distance had Hazel covered than Seth 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 4.20 p.m. to 8 p.m. = 3 h 40 min = 3²₃ h
Duration from 4.20 p.m. to 8 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 Hazel
= 80 x 3¹₂
= 80 x ⁷₂ 
= 280 km

Distance covered by Seth
= 69 x 3¹₂
= 69 x ⁷₂
= 253 km

Distance that Hazel covered more than Seth
= 280 - 253
= 27 km

(b)
Distance between Hotel K and Hotel L
= (280 + 253) ÷ 2
= 533 ÷ 2
= 266¹₂ km

Answer(s): (a) 27 km; (b) 266¹₂ km