At 3.35 p.m., Opal and Mark left Hotel T for Hotel U at average speeds of 72 km/h and 60 km/h respectively. Upon reaching Hotel U, Opal rested for 15 minutes. She then headed back for Hotel T at an average speed of 72 km/h along the same route. Mark and Opal met each other on their way at 7 p.m.

1. How much more distance had Opal covered than Mark when they met on their way?
2. How far apart were Hotel T and Hotel U? Express your answer in mixed number.

(a)
Duration from 3.35 p.m. to 7 p.m. = 3 h 25 min = 3⁵₁₂ h
Duration from 3.35 p.m. to 7 p.m. without 15 min rest = 3 h 10 min = 3¹₆ h

60 min = 1 h
25 min = ²⁵₆₀ = ⁵₁₂ h
10 min = ¹⁰₆₀ = ¹₆ h


Distance covered by Opal
= 72 x 3¹₆
= 72 x ¹⁹₆ 
= 228 km

Distance covered by Mark
= 60 x 3¹₆
= 60 x ¹⁹₆
= 205 km

Distance that Opal covered more than Mark
= 228 - 205
= 23 km

(b)
Distance between Hotel T and Hotel U
= (228 + 205) ÷ 2
= 433 ÷ 2
= 216¹₂ km

Answer(s): (a) 23 km; (b) 216¹₂ km