At 2.30 p.m., Fiona and Henry left Hotel N for Hotel P at average speeds of 96 km/h and 74 km/h respectively. Upon reaching Hotel P, Fiona rested for 25 minutes. She then headed back for Hotel N at an average speed of 96 km/h along the same route. Henry and Fiona met each other on their way at 6 p.m.

1. How much more distance had Fiona covered than Henry when they met on their way?
2. How far apart were Hotel N and Hotel P? 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 25 min rest = 3 h 5 min = 3¹₁₂ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
5 min = ⁵₆₀ = ¹₁₂ h


Distance covered by Fiona
= 96 x 3¹₁₂
= 96 x ³⁷₁₂ 
= 296 km

Distance covered by Henry
= 74 x 3¹₁₂
= 74 x ³⁷₁₂
= 259 km

Distance that Fiona covered more than Henry
= 296 - 259
= 37 km

(b)
Distance between Hotel N and Hotel P
= (296 + 259) ÷ 2
= 555 ÷ 2
= 277¹₂ km

Answer(s): (a) 37 km; (b) 277¹₂ km