Ken and Paul took part in a 42 km marathon. Ken 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. Paul 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 4.30 a.m., at what time would each of them finish?
- Ken
- Paul
(a)
Half of the 42 km marathon = 42 ÷ 2 = 21 km
Time taken by Ken for the first half of the marathon
= 21 ÷ 12
= 1
34 h
Time taken by Ken for the last half of the marathon
= 21 ÷ 5
= 4
15 h
Total time taken by Ken
= 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 4.30 a.m. = 10.27 a.m.
Time that Ken would finish the marathon = 10.27 a.m.
(b)
Time taken by Paul for the first half of the marathon
= 21 ÷ 10
= 2
110 h
Time taken by Paul for the last half of the marathon
= 21 ÷ 9
= 2
13 h
Total time taken by Paul
= 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 4.30 a.m. = 8.56 a.m.
Time that Paul would finish the marathon = 8.56 a.m.
Answer(s): (a) 10.27 a.m.; (b) 8.56 a.m.