Vaidev and Zeph took part in a 32 km marathon. Vaidev ran half the distance at a speed of 8 km/h and ran slower for the rest of the way at a speed of 6 km/h. Zeph ran half his total time at 10 km/h and ran slower for the rest of the time at 6 km/h. If they started the marathon at 5.30 a.m., at what time would each of them finish?

1. Vaidev
2. Zeph

(a)
Half of the 32 km marathon = 32 ÷ 2 = 16 km

Time taken by Vaidev for the first half of the marathon
= 16 ÷ 8
= 2 h

Time taken by Vaidev for the last half of the marathon
= 16 ÷ 6
= 2²₃ h

Total time taken by Vaidev
= 2 + 2²₃
= 4²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
4²₃ h = 4 h 40 min

4 h 40 min after 5.30 a.m. = 10.10 a.m.
Time that Vaidev would finish the marathon = 10.10 a.m.

(b)
Time taken by Zeph for the first half of the marathon
= 16 ÷ 10
= 1³₅ h

Time taken by Zeph for the last half of the marathon
= 16 ÷ 6
= 2²₃ h

Total time taken by Zeph
= 1³₅ + 2²₃
= 4⁴₁₅ h

1 h = 60 min
⁴₁₅ h = ⁴₁₅ x 60 = 16 min
4⁴₁₅ h = 4 h 16 min
4 h 16 min after 5.30 a.m. = 9.46 a.m.
Time that Zeph would finish the marathon = 9.46 a.m.

Answer(s): (a) 10.10 a.m.; (b) 9.46 a.m.