At 3.20 p.m., Dana and Paul left Hotel K for Hotel L at average speeds of 100 km/h and 63 km/h respectively. Upon reaching Hotel L, Dana rested for 10 minutes. She then headed back for Hotel K at an average speed of 100 km/h along the same route. Paul and Dana met each other on their way at 7 p.m.

1. How much more distance had Dana covered than Paul 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 3.20 p.m. to 7 p.m. = 3 h 40 min = 3²₃ h
Duration from 3.20 p.m. to 7 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 Dana
= 100 x 3¹₂
= 100 x ⁷₂ 
= 350 km

Distance covered by Paul
= 63 x 3¹₂
= 63 x ⁷₂
= 231 km

Distance that Dana covered more than Paul
= 350 - 231
= 119 km

(b)
Distance between Hotel K and Hotel L
= (350 + 231) ÷ 2
= 581 ÷ 2
= 290¹₂ km

Answer(s): (a) 119 km; (b) 290¹₂ km