Andy and Justin took part in a 42 km marathon. Andy ran half the distance at a speed of 12 km/h and ran slower for the rest of the way at a speed of 5 km/h. Justin 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 4.30 a.m., at what time would each of them finish?

1. Andy
2. Justin

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

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

Time taken by Andy for the last half of the marathon
= 21 ÷ 5
= 4¹₅ h

Total time taken by Andy
= 1³₄ + 4¹₅
= 5¹⁹₂₀ h

1 h = 60 min
¹⁹₂₀ h = ¹⁹₂₀ x 60 = 57 min
5¹⁹₂₀ h = 5 h 57 min

5 h 57 min after 4.30 a.m. = 10.27 a.m.
Time that Andy would finish the marathon = 10.27 a.m.

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

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

Total time taken by Justin
= 1³₄ + 2¹₃
= 4¹₁₂ h

1 h = 60 min
¹₁₂ h = ¹₁₂ x 60 = 5 min
4¹₁₂ h = 4 h 5 min
4 h 5 min after 4.30 a.m. = 8.35 a.m.
Time that Justin would finish the marathon = 8.35 a.m.

Answer(s): (a) 10.27 a.m.; (b) 8.35 a.m.