Cole and Cody took part in a 42 km marathon. Cole 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. Cody ran half his total time at 10 km/h and ran slower for the rest of the time at 7 km/h. If they started the marathon at 3.30 a.m., at what time would each of them finish?

1. Cole
2. Cody

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

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

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

Total time taken by Cole
= 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 3.30 a.m. = 8.15 a.m.
Time that Cole would finish the marathon = 8.15 a.m.

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

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

Total time taken by Cody
= 2¹₁₀ + 3
= 5¹₁₀ h

1 h = 60 min
¹₁₀ h = ¹₁₀ x 60 = 6 min
5¹₁₀ h = 5 h 6 min
5 h 6 min after 3.30 a.m. = 8.36 a.m.
Time that Cody would finish the marathon = 8.36 a.m.

Answer(s): (a) 8.15 a.m.; (b) 8.36 a.m.