Liam and Mark took part in a 16 km marathon. Liam ran half the distance at a speed of 12 km/h and ran slower for the rest of the way at a speed of 8 km/h. Mark ran half his total time at 12 km/h and ran slower for the rest of the time at 5 km/h. If they started the marathon at 7.30 a.m., at what time would each of them finish?

1. Liam
2. Mark

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

Time taken by Liam for the first half of the marathon
= 8 ÷ 12
= ²₃ h

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

Total time taken by Liam
= ²₃ + 1
= 1²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
1²₃ h = 1 h 40 min

1 h 40 min after 7.30 a.m. = 9.10 a.m.
Time that Liam would finish the marathon = 9.10 a.m.

(b)
Time taken by Mark for the first half of the marathon
= 8 ÷ 12
= ²₃ h

Time taken by Mark for the last half of the marathon
= 8 ÷ 5
= 1³₅ h

Total time taken by Mark
= ²₃ + 1³₅
= 2⁴₁₅ h

1 h = 60 min
⁴₁₅ h = ⁴₁₅ x 60 = 16 min
2⁴₁₅ h = 2 h 16 min
2 h 16 min after 7.30 a.m. = 9.46 a.m.
Time that Mark would finish the marathon = 9.46 a.m.

Answer(s): (a) 9.10 a.m.; (b) 9.46 a.m.