Rael and Zeph took part in a 24 km marathon. Rael 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. Zeph ran half his total time at 10 km/h and ran slower for the rest of the time at 10 km/h. If they started the marathon at 4.30 a.m., at what time would each of them finish?

1. Rael
2. Zeph

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

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

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

Total time taken by Rael
= 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 4.30 a.m. = 8.14 a.m.
Time that Rael would finish the marathon = 8.14 a.m.

(b)
Time taken by Zeph for the first half of the marathon
= 12 ÷ 10
= 1¹₅ h

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

Total time taken by Zeph
= 1¹₅ + 1¹₅
= 2²₅ h

1 h = 60 min
²₅ h = ²₅ x 60 = 24 min
2²₅ h = 2 h 24 min
2 h 24 min after 4.30 a.m. = 6.54 a.m.
Time that Zeph would finish the marathon = 6.54 a.m.

Answer(s): (a) 8.14 a.m.; (b) 6.54 a.m.