At 1.20 p.m., Fanny and Elijah left Hotel S for Hotel T at average speeds of 94 km/h and 72 km/h respectively. Upon reaching Hotel T, Fanny rested for 10 minutes. She then headed back for Hotel S at an average speed of 94 km/h along the same route. Elijah and Fanny met each other on their way at 5 p.m.

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

(a)
Duration from 1.20 p.m. to 5 p.m. = 3 h 40 min = 3²₃ h
Duration from 1.20 p.m. to 5 p.m. without 10 min rest = 3 h 30 min = 3¹₂ h

60 min = 1 h
40 min = ⁴⁰₆₀ = ²₃ h
30 min = ³⁰₆₀ = ¹₂ h


Distance covered by Fanny
= 94 x 3¹₂
= 94 x ⁷₂ 
= 329 km

Distance covered by Elijah
= 72 x 3¹₂
= 72 x ⁷₂
= 264 km

Distance that Fanny covered more than Elijah
= 329 - 264
= 65 km

(b)
Distance between Hotel S and Hotel T
= (329 + 264) ÷ 2
= 593 ÷ 2
= 296¹₂ km

Answer(s): (a) 65 km; (b) 296¹₂ km