David and Oliver took part in a 42 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 5 km/h. Oliver 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 6.30 a.m., at what time would each of them finish?
- David
- Oliver
(a)
Half of the 42 km marathon = 42 ÷ 2 = 21 km
Time taken by David for the first half of the marathon
= 21 ÷ 12
= 1
34 h
Time taken by David for the last half of the marathon
= 21 ÷ 5
= 4
15 h
Total time taken by David
= 1
34 + 4
15= 5
1920 h
1 h = 60 min
1920 h =
1920 x 60 = 57 min
5
1920 h = 5 h 57 min
5 h 57 min after 6.30 a.m. = 12.27 a.m.
Time that David would finish the marathon = 12.27 a.m.
(b)
Time taken by Oliver for the first half of the marathon
= 21 ÷ 10
= 2
110 h
Time taken by Oliver for the last half of the marathon
= 21 ÷ 10
= 2
110 h
Total time taken by Oliver
= 2
110 + 2
110 = 4
210 h
1 h = 60 min
210 h =
210 x 60 = 12 min
4
210 h = 4 h 12 min
4 h 12 min after 6.30 a.m. = 10.42 a.m.
Time that Oliver would finish the marathon = 10.42 a.m.
Answer(s): (a) 12.27 a.m.; (b) 10.42 a.m.