At 3.30 p.m., Julie and Tommy left Hotel X for Hotel Y at average speeds of 84 km/h and 64 km/h respectively. Upon reaching Hotel Y, Julie rested for 25 minutes. She then headed back for Hotel X at an average speed of 84 km/h along the same route. Tommy and Julie met each other on their way at 7 p.m.

1. How much more distance had Julie covered than Tommy when they met on their way?
2. How far apart were Hotel X and Hotel Y? Express your answer in mixed number.

(a)
Duration from 3.30 p.m. to 7 p.m. = 3 h 30 min = 3¹₂ h
Duration from 3.30 p.m. to 7 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 Julie
= 84 x 3¹₁₂
= 84 x ³⁷₁₂ 
= 259 km

Distance covered by Tommy
= 64 x 3¹₁₂
= 64 x ³⁷₁₂
= 224 km

Distance that Julie covered more than Tommy
= 259 - 224
= 35 km

(b)
Distance between Hotel X and Hotel Y
= (259 + 224) ÷ 2
= 483 ÷ 2
= 241¹₂ km

Answer(s): (a) 35 km; (b) 241¹₂ km