Luke and Sam took part in a 24 km marathon. Luke ran half the distance at a speed of 10 km/h and ran slower for the rest of the way at a speed of 8 km/h. Sam ran half his total time at 10 km/h and ran slower for the rest of the time at 6 km/h. If they started the marathon at 5.30 a.m., at what time would each of them finish?

1. Luke
2. Sam

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

Time taken by Luke for the first half of the marathon
= 12 ÷ 10
= 1¹₅ h

Time taken by Luke for the last half of the marathon
= 12 ÷ 8
= 1¹₂ h

Total time taken by Luke
= 1¹₅ + 1¹₂
= 2⁷₁₀ h

1 h = 60 min
⁷₁₀ h = ⁷₁₀ x 60 = 42 min
2⁷₁₀ h = 2 h 42 min

2 h 42 min after 5.30 a.m. = 8.12 a.m.
Time that Luke would finish the marathon = 8.12 a.m.

(b)
Time taken by Sam for the first half of the marathon
= 12 ÷ 10
= 1¹₅ h

Time taken by Sam for the last half of the marathon
= 12 ÷ 6
= 2 h

Total time taken by Sam
= 1¹₅ + 2
= 3¹₅ h

1 h = 60 min
¹₅ h = ¹₅ x 60 = 12 min
3¹₅ h = 3 h 12 min
3 h 12 min after 5.30 a.m. = 8.42 a.m.
Time that Sam would finish the marathon = 8.42 a.m.

Answer(s): (a) 8.12 a.m.; (b) 8.42 a.m.