City R and City S is 525 km apart. Elijah left City R for City S at 9.00 a.m. travelling at an average speed of 75 km/h. Mark left City R later than Elijah and caught up with him at 12.00 p.m. Mark was travelling at a speed of 90 km/h.

1. At what time did Mark leave City R?
2. How much later did Elijah arrive in City S than Mark? Express your answer in h as a fraction or mixed number.

(a)
From 9.00 a.m. to 12.00 p.m. = 3 h

Distance that Elijah covered when Mark caught up with Elijah
= 3 x 75
= 225 km

Time that Mark took to travel 225 km
= 225 ÷ 90
= 2¹₂ h

1 h = 60 min
¹₂ h = ¹₂ x 60 = 30 min
2¹₂ h = 2 h 30 min

Time that Mark left City R:
2 h 30 min before 12.00 p.m. = 9.30 a.m.

(b)
Remaining distance that they had to cover to reach City S
= 525 - 225
= 300 km

Duration that Mark had to travel before reaching City S
= 300 ÷ 90
= 3¹₃ h

Duration that Elijah had to travel before reaching City S
= 300 ÷ 75
= 4 h

Duration that Elijah took to arrive later than Mark in City S
= 4 - 3¹₃
= ²₃ h

Answer(s): (a) 9.30 a.m.; (b) ²₃ h