At 1.30 p.m., Penelope and Reggie left Hotel J for Hotel K at average speeds of 72 km/h and 50 km/h respectively. Upon reaching Hotel K, Penelope rested for 25 minutes. She then headed back for Hotel J at an average speed of 72 km/h along the same route. Reggie and Penelope met each other on their way at 5 p.m.

1. How much more distance had Penelope covered than Reggie when they met on their way?
2. How far apart were Hotel J and Hotel K? Express your answer in mixed number.

(a)
Duration from 1.30 p.m. to 5 p.m. = 3 h 30 min = 3¹₂ h
Duration from 1.30 p.m. to 5 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 Penelope
= 72 x 3¹₁₂
= 72 x ³⁷₁₂ 
= 222 km

Distance covered by Reggie
= 50 x 3¹₁₂
= 50 x ³⁷₁₂
= 175 km

Distance that Penelope covered more than Reggie
= 222 - 175
= 47 km

(b)
Distance between Hotel J and Hotel K
= (222 + 175) ÷ 2
= 397 ÷ 2
= 198¹₂ km

Answer(s): (a) 47 km; (b) 198¹₂ km