Fred and Ryan took part in a 24 km marathon. Fred ran half the distance at a speed of 9 km/h and ran slower for the rest of the way at a speed of 5 km/h. Ryan 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 7.30 a.m., at what time would each of them finish?

1. Fred
2. Ryan

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

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

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

Total time taken by Fred
= 1¹₃ + 2²₅
= 3¹¹₁₅ h

1 h = 60 min
¹¹₁₅ h = ¹¹₁₅ x 60 = 44 min
3¹¹₁₅ h = 3 h 44 min

3 h 44 min after 7.30 a.m. = 11.14 a.m.
Time that Fred would finish the marathon = 11.14 a.m.

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

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

Total time taken by Ryan
= 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 7.30 a.m. = 9.50 a.m.
Time that Ryan would finish the marathon = 9.50 a.m.

Answer(s): (a) 11.14 a.m.; (b) 9.50 a.m.