Ben and Jeremy took part in a 42 km marathon. Ben ran half the distance at a speed of 9 km/h and ran slower for the rest of the way at a speed of 9 km/h. Jeremy ran half his total time at 12 km/h and ran slower for the rest of the time at 6 km/h. If they started the marathon at 7.30 a.m., at what time would each of them finish?

1. Ben
2. Jeremy

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

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

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

Total time taken by Ben
= 2¹₃ + 2¹₃
= 4²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
4²₃ h = 4 h 40 min

4 h 40 min after 7.30 a.m. = 12.10 a.m.
Time that Ben would finish the marathon = 12.10 a.m.

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

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

Total time taken by Jeremy
= 1³₄ + 3¹₂
= 5¹₄ h

1 h = 60 min
¹₄ h = ¹₄ x 60 = 15 min
5¹₄ h = 5 h 15 min
5 h 15 min after 7.30 a.m. = 12.45 a.m.
Time that Jeremy would finish the marathon = 12.45 a.m.

Answer(s): (a) 12.10 a.m.; (b) 12.45 a.m.