City L and City M is 490 km apart. Fred left City L for City M at 7.00 a.m. travelling at an average speed of 70 km/h. Luke left City L later than Fred and caught up with him at 11.00 a.m. Luke was travelling at a speed of 96 km/h.

1. At what time did Luke leave City L?
2. How much later did Fred arrive in City M than Luke? 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 Fred covered when Luke caught up with Fred
= 4 x 70
= 280 km

Time that Luke took to travel 280 km
= 280 ÷ 96
= 2¹¹₁₂ h

1 h = 60 min
¹¹₁₂ h = ¹¹₁₂ x 60 = 55 min
2¹¹₁₂ h = 2 h 55 min

Time that Luke left City L:
2 h 55 min before 11.00 a.m. = 8.05 a.m.

(b)
Remaining distance that they had to cover to reach City M
= 490 - 280
= 210 km

Duration that Luke had to travel before reaching City M
= 210 ÷ 96
= 2³₁₆ h

Duration that Fred had to travel before reaching City M
= 210 ÷ 70
= 3 h

Duration that Fred took to arrive later than Luke in City M
= 3 - 2³₁₆
= ¹³₁₆ h

Answer(s): (a) 8.05 a.m.; (b) ¹³₁₆ h