David and Zane took part in a 16 km marathon. David ran half the distance at a speed of 12 km/h and ran slower for the rest of the way at a speed of 8 km/h. Zane ran half his total time at 12 km/h and ran slower for the rest of the time at 10 km/h. If they started the marathon at 5.30 a.m., at what time would each of them finish?
- David
- Zane
(a)
Half of the 16 km marathon = 16 ÷ 2 = 8 km
Time taken by David for the first half of the marathon
= 8 ÷ 12
=
23 h
Time taken by David for the last half of the marathon
= 8 ÷ 8
= 1 h
Total time taken by David
=
23 + 1
= 1
23 h
1 h = 60 min
23 h =
23 x 60 = 40 min
1
23 h = 1 h 40 min
1 h 40 min after 5.30 a.m. = 7.10 a.m.
Time that David would finish the marathon = 7.10 a.m.
(b)
Time taken by Zane for the first half of the marathon
= 8 ÷ 12
=
23 h
Time taken by Zane for the last half of the marathon
= 8 ÷ 10
=
45 h
Total time taken by Zane
=
23 +
45 = 1
715 h
1 h = 60 min
715 h =
715 x 60 = 28 min
1
715 h = 1 h 28 min
1 h 28 min after 5.30 a.m. = 6.58 a.m.
Time that Zane would finish the marathon = 6.58 a.m.
Answer(s): (a) 7.10 a.m.; (b) 6.58 a.m.