Ken and Julian took part in a 24 km marathon. Ken 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. Julian 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 7.30 a.m., at what time would each of them finish?

1. Ken
2. Julian

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

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

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

Total time taken by Ken
= 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 7.30 a.m. = 10.10 a.m.
Time that Ken would finish the marathon = 10.10 a.m.

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

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

Total time taken by Julian
= 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 7.30 a.m. = 9.42 a.m.
Time that Julian would finish the marathon = 9.42 a.m.

Answer(s): (a) 10.10 a.m.; (b) 9.42 a.m.