Carl and Valen took part in a 32 km marathon. Carl 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. Valen 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 3.30 a.m., at what time would each of them finish?

1. Carl
2. Valen

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

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

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

Total time taken by Carl
= 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 3.30 a.m. = 8.10 a.m.
Time that Carl would finish the marathon = 8.10 a.m.

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

Time taken by Valen for the last half of the marathon
= 16 ÷ 10
= 1³₅ h

Total time taken by Valen
= 1³₅ + 1³₅
= 3¹₅ h

1 h = 60 min
¹₅ h = ¹₅ x 60 = 12 min
3¹₅ h = 3 h 12 min
3 h 12 min after 3.30 a.m. = 6.42 a.m.
Time that Valen would finish the marathon = 6.42 a.m.

Answer(s): (a) 8.10 a.m.; (b) 6.42 a.m.