Billy and Riordan took part in a 24 km marathon. Billy 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. Riordan ran half his total time at 12 km/h and ran slower for the rest of the time at 9 km/h. If they started the marathon at 6.30 a.m., at what time would each of them finish?
- Billy
- Riordan
(a)
Half of the 24 km marathon = 24 ÷ 2 = 12 km
Time taken by Billy for the first half of the marathon
= 12 ÷ 9
= 1
13 h
Time taken by Billy for the last half of the marathon
= 12 ÷ 8
= 1
12 h
Total time taken by Billy
= 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 6.30 a.m. = 9.20 a.m.
Time that Billy would finish the marathon = 9.20 a.m.
(b)
Time taken by Riordan for the first half of the marathon
= 12 ÷ 12
= 1 h
Time taken by Riordan for the last half of the marathon
= 12 ÷ 9
= 1
13 h
Total time taken by Riordan
= 1 + 1
13 = 2
13 h
1 h = 60 min
13 h =
13 x 60 = 20 min
2
13 h = 2 h 20 min
2 h 20 min after 6.30 a.m. = 8.50 a.m.
Time that Riordan would finish the marathon = 8.50 a.m.
Answer(s): (a) 9.20 a.m.; (b) 8.50 a.m.