Fabian and Asher took part in a 42 km marathon. Fabian ran half the distance at a speed of 9 km/h and ran slower for the rest of the way at a speed of 6 km/h. Asher 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. Fabian
2. Asher

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

Time taken by Fabian for the first half of the marathon
= 21 ÷ 9
= 2¹₃ h

Time taken by Fabian for the last half of the marathon
= 21 ÷ 6
= 3¹₂ h

Total time taken by Fabian
= 2¹₃ + 3¹₂
= 5⁵₆ h

1 h = 60 min
⁵₆ h = ⁵₆ x 60 = 50 min
5⁵₆ h = 5 h 50 min

5 h 50 min after 4.30 a.m. = 10.20 a.m.
Time that Fabian would finish the marathon = 10.20 a.m.

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

Time taken by Asher for the last half of the marathon
= 21 ÷ 10
= 2¹₁₀ h

Total time taken by Asher
= 2¹₁₀ + 2¹₁₀
= 4²₁₀ h

1 h = 60 min
²₁₀ h = ²₁₀ x 60 = 12 min
4²₁₀ h = 4 h 12 min
4 h 12 min after 4.30 a.m. = 8.42 a.m.
Time that Asher would finish the marathon = 8.42 a.m.

Answer(s): (a) 10.20 a.m.; (b) 8.42 a.m.