Ethan and Peter took part in a 16 km marathon. Ethan 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. Peter 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 6.30 a.m., at what time would each of them finish?

1. Ethan
2. Peter

(a)
Half of the 16 km marathon = 16 ÷ 2 = 8 km

Time taken by Ethan for the first half of the marathon
= 8 ÷ 10
= ⁴₅ h

Time taken by Ethan for the last half of the marathon
= 8 ÷ 8
= 1 h

Total time taken by Ethan
= ⁴₅ + 1
= 1⁴₅ h

1 h = 60 min
⁴₅ h = ⁴₅ x 60 = 48 min
1⁴₅ h = 1 h 48 min

1 h 48 min after 6.30 a.m. = 8.18 a.m.
Time that Ethan would finish the marathon = 8.18 a.m.

(b)
Time taken by Peter for the first half of the marathon
= 8 ÷ 10
= ⁴₅ h

Time taken by Peter for the last half of the marathon
= 8 ÷ 6
= 1¹₃ h

Total time taken by Peter
= ⁴₅ + 1¹₃
= 2²₁₅ h

1 h = 60 min
²₁₅ h = ²₁₅ x 60 = 8 min
2²₁₅ h = 2 h 8 min
2 h 8 min after 6.30 a.m. = 8.38 a.m.
Time that Peter would finish the marathon = 8.38 a.m.

Answer(s): (a) 8.18 a.m.; (b) 8.38 a.m.