At 1.40 p.m., Tammy and Vincent left Hotel E for Hotel F at average speeds of 78 km/h and 60 km/h respectively. Upon reaching Hotel F, Tammy rested for 10 minutes. She then headed back for Hotel E at an average speed of 78 km/h along the same route. Vincent and Tammy met each other on their way at 5 p.m.

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

(a)
Duration from 1.40 p.m. to 5 p.m. = 3 h 20 min = 3¹₃ h
Duration from 1.40 p.m. to 5 p.m. without 10 min rest = 3 h 10 min = 3¹₆ h

60 min = 1 h
20 min = ²⁰₆₀ = ¹₃ h
10 min = ¹⁰₆₀ = ¹₆ h


Distance covered by Tammy
= 78 x 3¹₆
= 78 x ¹⁹₆ 
= 247 km

Distance covered by Vincent
= 60 x 3¹₆
= 60 x ¹⁹₆
= 200 km

Distance that Tammy covered more than Vincent
= 247 - 200
= 47 km

(b)
Distance between Hotel E and Hotel F
= (247 + 200) ÷ 2
= 447 ÷ 2
= 223¹₂ km

Answer(s): (a) 47 km; (b) 223¹₂ km