Archie and Harry took part in a 42 km marathon. Archie 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. Harry ran half his total time at 12 km/h and ran slower for the rest of the time at 6 km/h. If they started the marathon at 3.30 a.m., at what time would each of them finish?

1. Archie
2. Harry

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

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

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

Total time taken by Archie
= 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 3.30 a.m. = 9.20 a.m.
Time that Archie would finish the marathon = 9.20 a.m.

(b)
Time taken by Harry for the first half of the marathon
= 21 ÷ 12
= 1³₄ h

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

Total time taken by Harry
= 1³₄ + 3¹₂
= 5¹₄ h

1 h = 60 min
¹₄ h = ¹₄ x 60 = 15 min
5¹₄ h = 5 h 15 min
5 h 15 min after 3.30 a.m. = 8.45 a.m.
Time that Harry would finish the marathon = 8.45 a.m.

Answer(s): (a) 9.20 a.m.; (b) 8.45 a.m.