At 4.30 p.m., Eva and Cody left Hotel X for Hotel Y at average speeds of 99 km/h and 70 km/h respectively. Upon reaching Hotel Y, Eva rested for 10 minutes. She then headed back for Hotel X at an average speed of 99 km/h along the same route. Cody and Eva met each other on their way at 8 p.m.

1. How much more distance had Eva covered than Cody 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 4.30 p.m. to 8 p.m. = 3 h 30 min = 3¹₂ h
Duration from 4.30 p.m. to 8 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 Eva
= 99 x 3¹₃
= 99 x ¹⁰₃ 
= 330 km

Distance covered by Cody
= 70 x 3¹₃
= 70 x ¹⁰₃
= 245 km

Distance that Eva covered more than Cody
= 330 - 245
= 85 km

(b)
Distance between Hotel X and Hotel Y
= (330 + 245) ÷ 2
= 575 ÷ 2
= 287¹₂ km

Answer(s): (a) 85 km; (b) 287¹₂ km