Riordan and Ian took part in a 24 km marathon. Riordan ran half the distance at a speed of 8 km/h and ran slower for the rest of the way at a speed of 9 km/h. Ian ran half his total time at 12 km/h and ran slower for the rest of the time at 5 km/h. If they started the marathon at 7.30 a.m., at what time would each of them finish?

1. Riordan
2. Ian

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

Time taken by Riordan for the first half of the marathon
= 12 ÷ 8
= 1¹₂ h

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

Total time taken by Riordan
= 1¹₂ + 1¹₃
= 2⁵₆ h

1 h = 60 min
⁵₆ h = ⁵₆ x 60 = 50 min
2⁵₆ h = 2 h 50 min

2 h 50 min after 7.30 a.m. = 10.20 a.m.
Time that Riordan would finish the marathon = 10.20 a.m.

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

Time taken by Ian for the last half of the marathon
= 12 ÷ 5
= 2²₅ h

Total time taken by Ian
= 1 + 2²₅
= 3²₅ h

1 h = 60 min
²₅ h = ²₅ x 60 = 24 min
3²₅ h = 3 h 24 min
3 h 24 min after 7.30 a.m. = 10.54 a.m.
Time that Ian would finish the marathon = 10.54 a.m.

Answer(s): (a) 10.20 a.m.; (b) 10.54 a.m.