Ivan and Pierre took part in a 42 km marathon. Ivan ran half the distance at a speed of 12 km/h and ran slower for the rest of the way at a speed of 7 km/h. Pierre 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 3.30 a.m., at what time would each of them finish?
- Ivan
- Pierre
(a)
Half of the 42 km marathon = 42 ÷ 2 = 21 km
Time taken by Ivan for the first half of the marathon
= 21 ÷ 12
= 1
34 h
Time taken by Ivan for the last half of the marathon
= 21 ÷ 7
= 3 h
Total time taken by Ivan
= 1
34 + 3
= 4
34 h
1 h = 60 min
34 h =
34 x 60 = 45 min
4
34 h = 4 h 45 min
4 h 45 min after 3.30 a.m. = 8.15 a.m.
Time that Ivan would finish the marathon = 8.15 a.m.
(b)
Time taken by Pierre for the first half of the marathon
= 21 ÷ 10
= 2
110 h
Time taken by Pierre for the last half of the marathon
= 21 ÷ 10
= 2
110 h
Total time taken by Pierre
= 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 3.30 a.m. = 7.42 a.m.
Time that Pierre would finish the marathon = 7.42 a.m.
Answer(s): (a) 8.15 a.m.; (b) 7.42 a.m.