Brandon and Gabriel took part in a 16 km marathon. Brandon ran half the distance at a speed of 12 km/h and ran slower for the rest of the way at a speed of 8 km/h. Gabriel 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 4.30 a.m., at what time would each of them finish?

1. Brandon
2. Gabriel

(a)
Half of the 16 km marathon = 16 ÷ 2 = 8 km

Time taken by Brandon for the first half of the marathon
= 8 ÷ 12
= ²₃ h

Time taken by Brandon for the last half of the marathon
= 8 ÷ 8
= 1 h

Total time taken by Brandon
= ²₃ + 1
= 1²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
1²₃ h = 1 h 40 min

1 h 40 min after 4.30 a.m. = 6.10 a.m.
Time that Brandon would finish the marathon = 6.10 a.m.

(b)
Time taken by Gabriel for the first half of the marathon
= 8 ÷ 10
= ⁴₅ h

Time taken by Gabriel for the last half of the marathon
= 8 ÷ 6
= 1¹₃ h

Total time taken by Gabriel
= ⁴₅ + 1¹₃
= 2²₁₅ h

1 h = 60 min
²₁₅ h = ²₁₅ x 60 = 8 min
2²₁₅ h = 2 h 8 min
2 h 8 min after 4.30 a.m. = 6.38 a.m.
Time that Gabriel would finish the marathon = 6.38 a.m.

Answer(s): (a) 6.10 a.m.; (b) 6.38 a.m.