Elijah and Albert took part in a 24 km marathon. Elijah ran half the distance at a speed of 9 km/h and ran slower for the rest of the way at a speed of 9 km/h. Albert ran half his total time at 10 km/h and ran slower for the rest of the time at 6 km/h. If they started the marathon at 6.30 a.m., at what time would each of them finish?

1. Elijah
2. Albert

(a)
Half of the 24 km marathon = 24 ÷ 2 = 12 km

Time taken by Elijah for the first half of the marathon
= 12 ÷ 9
= 1¹₃ h

Time taken by Elijah for the last half of the marathon
= 12 ÷ 9
= 1¹₃ h

Total time taken by Elijah
= 1¹₃ + 1¹₃
= 2²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
2²₃ h = 2 h 40 min

2 h 40 min after 6.30 a.m. = 9.10 a.m.
Time that Elijah would finish the marathon = 9.10 a.m.

(b)
Time taken by Albert for the first half of the marathon
= 12 ÷ 10
= 1¹₅ h

Time taken by Albert for the last half of the marathon
= 12 ÷ 6
= 2 h

Total time taken by Albert
= 1¹₅ + 2
= 3¹₅ h

1 h = 60 min
¹₅ h = ¹₅ x 60 = 12 min
3¹₅ h = 3 h 12 min
3 h 12 min after 6.30 a.m. = 9.42 a.m.
Time that Albert would finish the marathon = 9.42 a.m.

Answer(s): (a) 9.10 a.m.; (b) 9.42 a.m.