At 5.20 p.m., Diana and Ryan left Hotel K for Hotel L at average speeds of 82 km/h and 60 km/h respectively. Upon reaching Hotel L, Diana rested for 10 minutes. She then headed back for Hotel K at an average speed of 82 km/h along the same route. Ryan and Diana met each other on their way at 9 p.m.

1. How much more distance had Diana covered than Ryan 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 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 Diana
= 82 x 3¹₂
= 82 x ⁷₂ 
= 287 km

Distance covered by Ryan
= 60 x 3¹₂
= 60 x ⁷₂
= 220 km

Distance that Diana covered more than Ryan
= 287 - 220
= 67 km

(b)
Distance between Hotel K and Hotel L
= (287 + 220) ÷ 2
= 507 ÷ 2
= 253¹₂ km

Answer(s): (a) 67 km; (b) 253¹₂ km