Tim and Caden took part in a 42 km marathon. Tim ran half the distance at a speed of 9 km/h and ran slower for the rest of the way at a speed of 9 km/h. Caden 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 4.30 a.m., at what time would each of them finish?

1. Tim
2. Caden

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

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

Time taken by Tim for the last half of the marathon
= 21 ÷ 9
= 2¹₃ h

Total time taken by Tim
= 2¹₃ + 2¹₃
= 4²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
4²₃ h = 4 h 40 min

4 h 40 min after 4.30 a.m. = 9.10 a.m.
Time that Tim would finish the marathon = 9.10 a.m.

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

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

Total time taken by Caden
= 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 4.30 a.m. = 9.36 a.m.
Time that Caden would finish the marathon = 9.36 a.m.

Answer(s): (a) 9.10 a.m.; (b) 9.36 a.m.