Warren and Owen took part in a 24 km marathon. Warren ran half the distance at a speed of 10 km/h and ran slower for the rest of the way at a speed of 8 km/h. Owen 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 5.30 a.m., at what time would each of them finish?

1. Warren
2. Owen

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

Time taken by Warren for the first half of the marathon
= 12 ÷ 10
= 1¹₅ h

Time taken by Warren for the last half of the marathon
= 12 ÷ 8
= 1¹₂ h

Total time taken by Warren
= 1¹₅ + 1¹₂
= 2⁷₁₀ h

1 h = 60 min
⁷₁₀ h = ⁷₁₀ x 60 = 42 min
2⁷₁₀ h = 2 h 42 min

2 h 42 min after 5.30 a.m. = 8.12 a.m.
Time that Warren would finish the marathon = 8.12 a.m.

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

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

Total time taken by Owen
= 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 5.30 a.m. = 8.54 a.m.
Time that Owen would finish the marathon = 8.54 a.m.

Answer(s): (a) 8.12 a.m.; (b) 8.54 a.m.