Ahmad and Pierre took part in a 42 km marathon. Ahmad 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. Pierre ran half his total time at 12 km/h and ran slower for the rest of the time at 9 km/h. If they started the marathon at 5.30 a.m., at what time would each of them finish?

1. Ahmad
2. Pierre

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

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

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

Total time taken by Ahmad
= 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 5.30 a.m. = 11.20 a.m.
Time that Ahmad would finish the marathon = 11.20 a.m.

(b)
Time taken by Pierre for the first half of the marathon
= 21 ÷ 12
= 1³₄ h

Time taken by Pierre for the last half of the marathon
= 21 ÷ 9
= 2¹₃ h

Total time taken by Pierre
= 1³₄ + 2¹₃
= 4¹₁₂ h

1 h = 60 min
¹₁₂ h = ¹₁₂ x 60 = 5 min
4¹₁₂ h = 4 h 5 min
4 h 5 min after 5.30 a.m. = 9.35 a.m.
Time that Pierre would finish the marathon = 9.35 a.m.

Answer(s): (a) 11.20 a.m.; (b) 9.35 a.m.