George and Tommy took part in a 24 km marathon. George ran half the distance at a speed of 9 km/h and ran slower for the rest of the way at a speed of 8 km/h. Tommy 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?
- George
- Tommy
(a)
Half of the 24 km marathon = 24 ÷ 2 = 12 km
Time taken by George for the first half of the marathon
= 12 ÷ 9
= 1
13 h
Time taken by George for the last half of the marathon
= 12 ÷ 8
= 1
12 h
Total time taken by George
= 1
13 + 1
12= 2
56 h
1 h = 60 min
56 h =
56 x 60 = 50 min
2
56 h = 2 h 50 min
2 h 50 min after 5.30 a.m. = 8.20 a.m.
Time that George would finish the marathon = 8.20 a.m.
(b)
Time taken by Tommy for the first half of the marathon
= 12 ÷ 12
= 1 h
Time taken by Tommy for the last half of the marathon
= 12 ÷ 5
= 2
25 h
Total time taken by Tommy
= 1 + 2
25 = 3
25 h
1 h = 60 min
25 h =
25 x 60 = 24 min
3
25 h = 3 h 24 min
3 h 24 min after 5.30 a.m. = 8.54 a.m.
Time that Tommy would finish the marathon = 8.54 a.m.
Answer(s): (a) 8.20 a.m.; (b) 8.54 a.m.