At 3.35 p.m., Diana and Japheth left Hotel J for Hotel K at average speeds of 96 km/h and 60 km/h respectively. Upon reaching Hotel K, Diana rested for 15 minutes. She then headed back for Hotel J at an average speed of 96 km/h along the same route. Japheth and Diana met each other on their way at 7 p.m.

1. How much more distance had Diana covered than Japheth when they met on their way?
2. How far apart were Hotel J and Hotel K? Express your answer in mixed number.

(a)
Duration from 3.35 p.m. to 7 p.m. = 3 h 25 min = 3⁵₁₂ h
Duration from 3.35 p.m. to 7 p.m. without 15 min rest = 3 h 10 min = 3¹₆ h

60 min = 1 h
25 min = ²⁵₆₀ = ⁵₁₂ h
10 min = ¹⁰₆₀ = ¹₆ h


Distance covered by Diana
= 96 x 3¹₆
= 96 x ¹⁹₆ 
= 304 km

Distance covered by Japheth
= 60 x 3¹₆
= 60 x ¹⁹₆
= 205 km

Distance that Diana covered more than Japheth
= 304 - 205
= 99 km

(b)
Distance between Hotel J and Hotel K
= (304 + 205) ÷ 2
= 509 ÷ 2
= 254¹₂ km

Answer(s): (a) 99 km; (b) 254¹₂ km