At 2.30 p.m., Xandra and Perry left Hotel K for Hotel L at average speeds of 76 km/h and 60 km/h respectively. Upon reaching Hotel L, Xandra rested for 15 minutes. She then headed back for Hotel K at an average speed of 76 km/h along the same route. Perry and Xandra met each other on their way at 6 p.m.

1. How much more distance had Xandra covered than Perry 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 2.30 p.m. to 6 p.m. = 3 h 30 min = 3¹₂ h
Duration from 2.30 p.m. to 6 p.m. without 15 min rest = 3 h 15 min = 3¹₄ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
15 min = ¹⁵₆₀ = ¹₄ h


Distance covered by Xandra
= 76 x 3¹₄
= 76 x ¹³₄ 
= 247 km

Distance covered by Perry
= 60 x 3¹₄
= 60 x ¹³₄
= 210 km

Distance that Xandra covered more than Perry
= 247 - 210
= 37 km

(b)
Distance between Hotel K and Hotel L
= (247 + 210) ÷ 2
= 457 ÷ 2
= 228¹₂ km

Answer(s): (a) 37 km; (b) 228¹₂ km