George and Caden took part in a 24 km marathon. George ran half the distance at a speed of 8 km/h and ran slower for the rest of the way at a speed of 5 km/h. Caden ran half his total time at 12 km/h and ran slower for the rest of the time at 9 km/h. If they started the marathon at 7.30 a.m., at what time would each of them finish?

1. George
2. Caden

(a)
Half of the 24 km marathon = 24 ÷ 2 = 12 km

Time taken by George for the first half of the marathon
= 12 ÷ 8
= 1¹₂ h

Time taken by George for the last half of the marathon
= 12 ÷ 5
= 2²₅ h

Total time taken by George
= 1¹₂ + 2²₅
= 3⁹₁₀ h

1 h = 60 min
⁹₁₀ h = ⁹₁₀ x 60 = 54 min
3⁹₁₀ h = 3 h 54 min

3 h 54 min after 7.30 a.m. = 11.24 a.m.
Time that George would finish the marathon = 11.24 a.m.

(b)
Time taken by Caden for the first half of the marathon
= 12 ÷ 12
= 1 h

Time taken by Caden for the last half of the marathon
= 12 ÷ 9
= 1¹₃ h

Total time taken by Caden
= 1 + 1¹₃
= 2¹₃ h

1 h = 60 min
¹₃ h = ¹₃ x 60 = 20 min
2¹₃ h = 2 h 20 min
2 h 20 min after 7.30 a.m. = 9.50 a.m.
Time that Caden would finish the marathon = 9.50 a.m.

Answer(s): (a) 11.24 a.m.; (b) 9.50 a.m.