Gabriel and Seth took part in a 42 km marathon. Gabriel ran half the distance at a speed of 12 km/h and ran slower for the rest of the way at a speed of 7 km/h. Seth 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 7.30 a.m., at what time would each of them finish?

1. Gabriel
2. Seth

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

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

Time taken by Gabriel for the last half of the marathon
= 21 ÷ 7
= 3 h

Total time taken by Gabriel
= 1³₄ + 3
= 4³₄ h

1 h = 60 min
³₄ h = ³₄ x 60 = 45 min
4³₄ h = 4 h 45 min

4 h 45 min after 7.30 a.m. = 12.15 a.m.
Time that Gabriel would finish the marathon = 12.15 a.m.

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

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

Total time taken by Seth
= 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 7.30 a.m. = 11.42 a.m.
Time that Seth would finish the marathon = 11.42 a.m.

Answer(s): (a) 12.15 a.m.; (b) 11.42 a.m.