At 1.30 p.m., Tammy and Ben left Hotel B for Hotel C at average speeds of 69 km/h and 52 km/h respectively. Upon reaching Hotel C, Tammy rested for 10 minutes. She then headed back for Hotel B at an average speed of 69 km/h along the same route. Ben and Tammy met each other on their way at 6 p.m.

1. How much more distance had Tammy covered than Ben when they met on their way?
2. How far apart were Hotel B and Hotel C? Express your answer in mixed number.

(a)
Duration from 1.30 p.m. to 6 p.m. = 4 h 30 min = 4¹₂ h
Duration from 1.30 p.m. to 6 p.m. without 10 min rest = 4 h 20 min = 4¹₃ h

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


Distance covered by Tammy
= 69 x 4¹₃
= 69 x ¹³₃ 
= 299 km

Distance covered by Ben
= 52 x 4¹₃
= 52 x ¹³₃
= 234 km

Distance that Tammy covered more than Ben
= 299 - 234
= 65 km

(b)
Distance between Hotel B and Hotel C
= (299 + 234) ÷ 2
= 533 ÷ 2
= 266¹₂ km

Answer(s): (a) 65 km; (b) 266¹₂ km