Valen and Mark took part in a 42 km marathon. Valen ran half the distance at a speed of 9 km/h and ran slower for the rest of the way at a speed of 6 km/h. Mark ran half his total time at 10 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. Valen
2. Mark

(a)
Half of the 42 km marathon = 42 ÷ 2 = 21 km

Time taken by Valen for the first half of the marathon
= 21 ÷ 9
= 2¹₃ h

Time taken by Valen for the last half of the marathon
= 21 ÷ 6
= 3¹₂ h

Total time taken by Valen
= 2¹₃ + 3¹₂
= 5⁵₆ h

1 h = 60 min
⁵₆ h = ⁵₆ x 60 = 50 min
5⁵₆ h = 5 h 50 min

5 h 50 min after 7.30 a.m. = 13.20 a.m.
Time that Valen would finish the marathon = 13.20 a.m.

(b)
Time taken by Mark for the first half of the marathon
= 21 ÷ 10
= 2¹₁₀ h

Time taken by Mark for the last half of the marathon
= 21 ÷ 5
= 4¹₅ h

Total time taken by Mark
= 2¹₁₀ + 4¹₅
= 6³₁₀ h

1 h = 60 min
³₁₀ h = ³₁₀ x 60 = 18 min
6³₁₀ h = 6 h 18 min
6 h 18 min after 7.30 a.m. = 13.48 a.m.
Time that Mark would finish the marathon = 13.48 a.m.

Answer(s): (a) 13.20 a.m.; (b) 13.48 a.m.