City L and City M is 456 km apart. Pierre left City L for City M at 11.00 a.m. travelling at an average speed of 76 km/h. Billy left City L later than Pierre and caught up with him at 1.00 p.m. Billy was travelling at a speed of 96 km/h.

1. At what time did Billy leave City L?
2. How much later did Pierre arrive in City M than Billy? Express your answer in h as a fraction or mixed number.

(a)
From 11.00 a.m. to 1.00 p.m. = 2 h

Distance that Pierre covered when Billy caught up with Pierre
= 2 x 76
= 152 km

Time that Billy took to travel 152 km
= 152 ÷ 96
= 1⁷₁₂ h

1 h = 60 min
⁷₁₂ h = ⁷₁₂ x 60 = 35 min
1⁷₁₂ h = 1 h 35 min

Time that Billy left City L:
1 h 35 min before 1.00 p.m. = 11.25 a.m.

(b)
Remaining distance that they had to cover to reach City M
= 456 - 152
= 304 km

Duration that Billy had to travel before reaching City M
= 304 ÷ 96
= 3¹₆ h

Duration that Pierre had to travel before reaching City M
= 304 ÷ 76
= 4 h

Duration that Pierre took to arrive later than Billy in City M
= 4 - 3¹₆
= ⁵₆ h

Answer(s): (a) 11.25 a.m.; (b) ⁵₆ h