At 2.40 p.m., Usha and Howard left Hotel J for Hotel K at average speeds of 84 km/h and 51 km/h respectively. Upon reaching Hotel K, Usha rested for 15 minutes. She then headed back for Hotel J at an average speed of 84 km/h along the same route. Howard and Usha met each other on their way at 6 p.m.

1. How much more distance had Usha covered than Howard 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 2.40 p.m. to 6 p.m. = 3 h 20 min = 3¹₃ h
Duration from 2.40 p.m. to 6 p.m. without 15 min rest = 3 h 5 min = 3¹₁₂ h

60 min = 1 h
20 min = ²⁰₆₀ = ¹₃ h
5 min = ⁵₆₀ = ¹₁₂ h


Distance covered by Usha
= 84 x 3¹₁₂
= 84 x ³⁷₁₂ 
= 259 km

Distance covered by Howard
= 51 x 3¹₁₂
= 51 x ³⁷₁₂
= 170 km

Distance that Usha covered more than Howard
= 259 - 170
= 89 km

(b)
Distance between Hotel J and Hotel K
= (259 + 170) ÷ 2
= 429 ÷ 2
= 214¹₂ km

Answer(s): (a) 89 km; (b) 214¹₂ km