At 2.30 p.m., Risa and Fred left Hotel N for Hotel P at average speeds of 84 km/h and 52 km/h respectively. Upon reaching Hotel P, Risa rested for 15 minutes. She then headed back for Hotel N at an average speed of 84 km/h along the same route. Fred and Risa met each other on their way at 7 p.m.

1. How much more distance had Risa covered than Fred 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 7 p.m. = 4 h 30 min = 4¹₂ h
Duration from 2.30 p.m. to 7 p.m. without 15 min rest = 4 h 15 min = 4¹₄ h

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


Distance covered by Risa
= 84 x 4¹₄
= 84 x ¹⁷₄ 
= 357 km

Distance covered by Fred
= 52 x 4¹₄
= 52 x ¹⁷₄
= 234 km

Distance that Risa covered more than Fred
= 357 - 234
= 123 km

(b)
Distance between Hotel N and Hotel P
= (357 + 234) ÷ 2
= 591 ÷ 2
= 295¹₂ km

Answer(s): (a) 123 km; (b) 295¹₂ km