Japheth and Fred took part in a 16 km marathon. Japheth ran half the distance at a speed of 10 km/h and ran slower for the rest of the way at a speed of 8 km/h. Fred ran half his total time at 12 km/h and ran slower for the rest of the time at 5 km/h. If they started the marathon at 5.30 a.m., at what time would each of them finish?
- Japheth
- Fred
(a)
Half of the 16 km marathon = 16 ÷ 2 = 8 km
Time taken by Japheth for the first half of the marathon
= 8 ÷ 10
=
45 h
Time taken by Japheth for the last half of the marathon
= 8 ÷ 8
= 1 h
Total time taken by Japheth
=
45 + 1
= 1
45 h
1 h = 60 min
45 h =
45 x 60 = 48 min
1
45 h = 1 h 48 min
1 h 48 min after 5.30 a.m. = 7.18 a.m.
Time that Japheth would finish the marathon = 7.18 a.m.
(b)
Time taken by Fred for the first half of the marathon
= 8 ÷ 12
=
23 h
Time taken by Fred for the last half of the marathon
= 8 ÷ 5
= 1
35 h
Total time taken by Fred
=
23 + 1
35 = 2
415 h
1 h = 60 min
415 h =
415 x 60 = 16 min
2
415 h = 2 h 16 min
2 h 16 min after 5.30 a.m. = 7.46 a.m.
Time that Fred would finish the marathon = 7.46 a.m.
Answer(s): (a) 7.18 a.m.; (b) 7.46 a.m.