Asher and Reggie took part in a 24 km marathon. Asher 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. Reggie ran half his total time at 12 km/h and ran slower for the rest of the time at 10 km/h. If they started the marathon at 4.30 a.m., at what time would each of them finish?

1. Asher
2. Reggie

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

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

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

Total time taken by Asher
= 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 4.30 a.m. = 7.10 a.m.
Time that Asher would finish the marathon = 7.10 a.m.

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

Time taken by Reggie for the last half of the marathon
= 12 ÷ 10
= 1¹₅ h

Total time taken by Reggie
= 1 + 1¹₅
= 2¹₅ h

1 h = 60 min
¹₅ h = ¹₅ x 60 = 12 min
2¹₅ h = 2 h 12 min
2 h 12 min after 4.30 a.m. = 6.42 a.m.
Time that Reggie would finish the marathon = 6.42 a.m.

Answer(s): (a) 7.10 a.m.; (b) 6.42 a.m.