Ethan and Bryan took part in a 32 km marathon. Ethan ran half the distance at a speed of 10 km/h and ran slower for the rest of the way at a speed of 5 km/h. Bryan 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. Ethan
2. Bryan

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

Time taken by Ethan for the first half of the marathon
= 16 ÷ 10
= 1³₅ h

Time taken by Ethan for the last half of the marathon
= 16 ÷ 5
= 3¹₅ h

Total time taken by Ethan
= 1³₅ + 3¹₅
= 4⁴₅ h

1 h = 60 min
⁴₅ h = ⁴₅ x 60 = 48 min
4⁴₅ h = 4 h 48 min

4 h 48 min after 3.30 a.m. = 8.18 a.m.
Time that Ethan would finish the marathon = 8.18 a.m.

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

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

Total time taken by Bryan
= 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 Bryan would finish the marathon = 6.42 a.m.

Answer(s): (a) 8.18 a.m.; (b) 6.42 a.m.