Vaidev and Archie took part in a 42 km marathon. Vaidev ran half the distance at a speed of 12 km/h and ran slower for the rest of the way at a speed of 5 km/h. Archie ran half his total time at 10 km/h and ran slower for the rest of the time at 5 km/h. If they started the marathon at 3.30 a.m., at what time would each of them finish?

1. Vaidev
2. Archie

(a)
Half of the 42 km marathon = 42 ÷ 2 = 21 km

Time taken by Vaidev for the first half of the marathon
= 21 ÷ 12
= 1³₄ h

Time taken by Vaidev for the last half of the marathon
= 21 ÷ 5
= 4¹₅ h

Total time taken by Vaidev
= 1³₄ + 4¹₅
= 5¹⁹₂₀ h

1 h = 60 min
¹⁹₂₀ h = ¹⁹₂₀ x 60 = 57 min
5¹⁹₂₀ h = 5 h 57 min

5 h 57 min after 3.30 a.m. = 9.27 a.m.
Time that Vaidev would finish the marathon = 9.27 a.m.

(b)
Time taken by Archie for the first half of the marathon
= 21 ÷ 10
= 2¹₁₀ h

Time taken by Archie for the last half of the marathon
= 21 ÷ 5
= 4¹₅ h

Total time taken by Archie
= 2¹₁₀ + 4¹₅
= 6³₁₀ h

1 h = 60 min
³₁₀ h = ³₁₀ x 60 = 18 min
6³₁₀ h = 6 h 18 min
6 h 18 min after 3.30 a.m. = 9.48 a.m.
Time that Archie would finish the marathon = 9.48 a.m.

Answer(s): (a) 9.27 a.m.; (b) 9.48 a.m.