Zane and Fred took part in a 42 km marathon. Zane 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. Fred ran half his total time at 10 km/h and ran slower for the rest of the time at 9 km/h. If they started the marathon at 3.30 a.m., at what time would each of them finish?
- Zane
- Fred
(a)
Half of the 42 km marathon = 42 ÷ 2 = 21 km
Time taken by Zane for the first half of the marathon
= 21 ÷ 9
= 2
13 h
Time taken by Zane for the last half of the marathon
= 21 ÷ 6
= 3
12 h
Total time taken by Zane
= 2
13 + 3
12= 5
56 h
1 h = 60 min
56 h =
56 x 60 = 50 min
5
56 h = 5 h 50 min
5 h 50 min after 3.30 a.m. = 9.20 a.m.
Time that Zane would finish the marathon = 9.20 a.m.
(b)
Time taken by Fred for the first half of the marathon
= 21 ÷ 10
= 2
110 h
Time taken by Fred for the last half of the marathon
= 21 ÷ 9
= 2
13 h
Total time taken by Fred
= 2
110 + 2
13 = 4
1330 h
1 h = 60 min
1330 h =
1330 x 60 = 26 min
4
1330 h = 4 h 26 min
4 h 26 min after 3.30 a.m. = 7.56 a.m.
Time that Fred would finish the marathon = 7.56 a.m.
Answer(s): (a) 9.20 a.m.; (b) 7.56 a.m.