City Y and City Z is 462 km apart. Henry left City Y for City Z at 7.00 a.m. travelling at an average speed of 66 km/h. Brandon left City Y later than Henry and caught up with him at 11.00 a.m. Brandon was travelling at a speed of 96 km/h.

1. At what time did Brandon leave City Y?
2. How much later did Henry arrive in City Z than Brandon? Express your answer in h as a fraction or mixed number.

(a)
From 7.00 a.m. to 11.00 a.m. = 4 h

Distance that Henry covered when Brandon caught up with Henry
= 4 x 66
= 264 km

Time that Brandon took to travel 264 km
= 264 ÷ 96
= 2³₄ h

1 h = 60 min
³₄ h = ³₄ x 60 = 45 min
2³₄ h = 2 h 45 min

Time that Brandon left City Y:
2 h 45 min before 11.00 a.m. = 8.15 a.m.

(b)
Remaining distance that they had to cover to reach City Z
= 462 - 264
= 198 km

Duration that Brandon had to travel before reaching City Z
= 198 ÷ 96
= 2¹₁₆ h

Duration that Henry had to travel before reaching City Z
= 198 ÷ 66
= 3 h

Duration that Henry took to arrive later than Brandon in City Z
= 3 - 2¹₁₆
= ¹⁵₁₆ h

Answer(s): (a) 8.15 a.m.; (b) ¹⁵₁₆ h