Archie and Ken took part in a 24 km marathon. Archie ran half the distance at a speed of 9 km/h and ran slower for the rest of the way at a speed of 8 km/h. Ken ran half his total time at 10 km/h and ran slower for the rest of the time at 10 km/h. If they started the marathon at 4.30 a.m., at what time would each of them finish?
- Archie
- Ken
(a)
Half of the 24 km marathon = 24 ÷ 2 = 12 km
Time taken by Archie for the first half of the marathon
= 12 ÷ 9
= 1
13 h
Time taken by Archie for the last half of the marathon
= 12 ÷ 8
= 1
12 h
Total time taken by Archie
= 1
13 + 1
12= 2
56 h
1 h = 60 min
56 h =
56 x 60 = 50 min
2
56 h = 2 h 50 min
2 h 50 min after 4.30 a.m. = 7.20 a.m.
Time that Archie would finish the marathon = 7.20 a.m.
(b)
Time taken by Ken for the first half of the marathon
= 12 ÷ 10
= 1
15 h
Time taken by Ken for the last half of the marathon
= 12 ÷ 10
= 1
15 h
Total time taken by Ken
= 1
15 + 1
15 = 2
25 h
1 h = 60 min
25 h =
25 x 60 = 24 min
2
25 h = 2 h 24 min
2 h 24 min after 4.30 a.m. = 6.54 a.m.
Time that Ken would finish the marathon = 6.54 a.m.
Answer(s): (a) 7.20 a.m.; (b) 6.54 a.m.