At 1.30 p.m., Diana and Nick left Hotel F for Hotel G at average speeds of 93 km/h and 78 km/h respectively. Upon reaching Hotel G, Diana rested for 10 minutes. She then headed back for Hotel F at an average speed of 93 km/h along the same route. Nick and Diana met each other on their way at 5 p.m.

1. How much more distance had Diana covered than Nick when they met on their way?
2. How far apart were Hotel F and Hotel G? 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 10 min rest = 3 h 20 min = 3¹₃ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
20 min = ²⁰₆₀ = ¹₃ h


Distance covered by Diana
= 93 x 3¹₃
= 93 x ¹⁰₃ 
= 310 km

Distance covered by Nick
= 78 x 3¹₃
= 78 x ¹⁰₃
= 273 km

Distance that Diana covered more than Nick
= 310 - 273
= 37 km

(b)
Distance between Hotel F and Hotel G
= (310 + 273) ÷ 2
= 583 ÷ 2
= 291¹₂ km

Answer(s): (a) 37 km; (b) 291¹₂ km