Luis and Japheth took part in a 32 km marathon. Luis ran half the distance at a speed of 10 km/h and ran slower for the rest of the way at a speed of 5 km/h. Japheth 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. Luis
2. Japheth

(a)
Half of the 32 km marathon = 32 ÷ 2 = 16 km

Time taken by Luis for the first half of the marathon
= 16 ÷ 10
= 1³₅ h

Time taken by Luis for the last half of the marathon
= 16 ÷ 5
= 3¹₅ h

Total time taken by Luis
= 1³₅ + 3¹₅
= 4⁴₅ h

1 h = 60 min
⁴₅ h = ⁴₅ x 60 = 48 min
4⁴₅ h = 4 h 48 min

4 h 48 min after 6.30 a.m. = 11.18 a.m.
Time that Luis would finish the marathon = 11.18 a.m.

(b)
Time taken by Japheth for the first half of the marathon
= 16 ÷ 10
= 1³₅ h

Time taken by Japheth for the last half of the marathon
= 16 ÷ 6
= 2²₃ h

Total time taken by Japheth
= 1³₅ + 2²₃
= 4⁴₁₅ h

1 h = 60 min
⁴₁₅ h = ⁴₁₅ x 60 = 16 min
4⁴₁₅ h = 4 h 16 min
4 h 16 min after 6.30 a.m. = 10.46 a.m.
Time that Japheth would finish the marathon = 10.46 a.m.

Answer(s): (a) 11.18 a.m.; (b) 10.46 a.m.