Reggie and Zeph took part in a 24 km marathon. Reggie ran half the distance at a speed of 8 km/h and ran slower for the rest of the way at a speed of 5 km/h. Zeph 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 4.30 a.m., at what time would each of them finish?

1. Reggie
2. Zeph

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

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

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

Total time taken by Reggie
= 1¹₂ + 2²₅
= 3⁹₁₀ h

1 h = 60 min
⁹₁₀ h = ⁹₁₀ x 60 = 54 min
3⁹₁₀ h = 3 h 54 min

3 h 54 min after 4.30 a.m. = 8.24 a.m.
Time that Reggie would finish the marathon = 8.24 a.m.

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

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

Total time taken by Zeph
= 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 4.30 a.m. = 6.50 a.m.
Time that Zeph would finish the marathon = 6.50 a.m.

Answer(s): (a) 8.24 a.m.; (b) 6.50 a.m.