Luis and Ahmad took part in a 24 km marathon. Luis 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. Ahmad ran half his total time at 12 km/h and ran slower for the rest of the time at 9 km/h. If they started the marathon at 6.30 a.m., at what time would each of them finish?

1. Luis
2. Ahmad

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

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

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

Total time taken by Luis
= 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 Luis would finish the marathon = 9.10 a.m.

(b)
Time taken by Ahmad for the first half of the marathon
= 12 ÷ 12
= 1 h

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

Total time taken by Ahmad
= 1 + 1¹₃
= 2¹₃ h

1 h = 60 min
¹₃ h = ¹₃ x 60 = 20 min
2¹₃ h = 2 h 20 min
2 h 20 min after 6.30 a.m. = 8.50 a.m.
Time that Ahmad would finish the marathon = 8.50 a.m.

Answer(s): (a) 9.10 a.m.; (b) 8.50 a.m.