Ivan and Billy took part in a 24 km marathon. Ivan 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. Billy ran half his total time at 12 km/h and ran slower for the rest of the time at 10 km/h. If they started the marathon at 3.30 a.m., at what time would each of them finish?

1. Ivan
2. Billy

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

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

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

Total time taken by Ivan
= 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 3.30 a.m. = 7.24 a.m.
Time that Ivan would finish the marathon = 7.24 a.m.

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

Time taken by Billy for the last half of the marathon
= 12 ÷ 10
= 1¹₅ h

Total time taken by Billy
= 1 + 1¹₅
= 2¹₅ h

1 h = 60 min
¹₅ h = ¹₅ x 60 = 12 min
2¹₅ h = 2 h 12 min
2 h 12 min after 3.30 a.m. = 5.42 a.m.
Time that Billy would finish the marathon = 5.42 a.m.

Answer(s): (a) 7.24 a.m.; (b) 5.42 a.m.