At 3.30 p.m., Erika and Ivan left Hotel H for Hotel J at average speeds of 96 km/h and 50 km/h respectively. Upon reaching Hotel J, Erika rested for 15 minutes. She then headed back for Hotel H at an average speed of 96 km/h along the same route. Ivan and Erika met each other on their way at 7 p.m.

1. How much more distance had Erika covered than Ivan when they met on their way?
2. How far apart were Hotel H and Hotel J? 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 15 min rest = 3 h 15 min = 3¹₄ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
15 min = ¹⁵₆₀ = ¹₄ h


Distance covered by Erika
= 96 x 3¹₄
= 96 x ¹³₄ 
= 312 km

Distance covered by Ivan
= 50 x 3¹₄
= 50 x ¹³₄
= 175 km

Distance that Erika covered more than Ivan
= 312 - 175
= 137 km

(b)
Distance between Hotel H and Hotel J
= (312 + 175) ÷ 2
= 487 ÷ 2
= 243¹₂ km

Answer(s): (a) 137 km; (b) 243¹₂ km