Tim and Owen took part in a 32 km marathon. Tim ran half the distance at a speed of 8 km/h and ran slower for the rest of the way at a speed of 6 km/h. Owen ran half his total time at 12 km/h and ran slower for the rest of the time at 8 km/h. If they started the marathon at 5.30 a.m., at what time would each of them finish?

1. Tim
2. Owen

(a)
Half of the 32 km marathon = 32 ÷ 2 = 16 km

Time taken by Tim for the first half of the marathon
= 16 ÷ 8
= 2 h

Time taken by Tim for the last half of the marathon
= 16 ÷ 6
= 2²₃ h

Total time taken by Tim
= 2 + 2²₃
= 4²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
4²₃ h = 4 h 40 min

4 h 40 min after 5.30 a.m. = 10.10 a.m.
Time that Tim would finish the marathon = 10.10 a.m.

(b)
Time taken by Owen for the first half of the marathon
= 16 ÷ 12
= 1¹₃ h

Time taken by Owen for the last half of the marathon
= 16 ÷ 8
= 2 h

Total time taken by Owen
= 1¹₃ + 2
= 3¹₃ h

1 h = 60 min
¹₃ h = ¹₃ x 60 = 20 min
3¹₃ h = 3 h 20 min
3 h 20 min after 5.30 a.m. = 8.50 a.m.
Time that Owen would finish the marathon = 8.50 a.m.

Answer(s): (a) 10.10 a.m.; (b) 8.50 a.m.