Tom and Nick took part in a 42 km marathon. Tom 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. Nick ran half his total time at 12 km/h and ran slower for the rest of the time at 6 km/h. If they started the marathon at 6.30 a.m., at what time would each of them finish?

1. Tom
2. Nick

(a)
Half of the 42 km marathon = 42 ÷ 2 = 21 km

Time taken by Tom for the first half of the marathon
= 21 ÷ 12
= 1³₄ h

Time taken by Tom for the last half of the marathon
= 21 ÷ 7
= 3 h

Total time taken by Tom
= 1³₄ + 3
= 4³₄ h

1 h = 60 min
³₄ h = ³₄ x 60 = 45 min
4³₄ h = 4 h 45 min

4 h 45 min after 6.30 a.m. = 11.15 a.m.
Time that Tom would finish the marathon = 11.15 a.m.

(b)
Time taken by Nick for the first half of the marathon
= 21 ÷ 12
= 1³₄ h

Time taken by Nick for the last half of the marathon
= 21 ÷ 6
= 3¹₂ h

Total time taken by Nick
= 1³₄ + 3¹₂
= 5¹₄ h

1 h = 60 min
¹₄ h = ¹₄ x 60 = 15 min
5¹₄ h = 5 h 15 min
5 h 15 min after 6.30 a.m. = 11.45 a.m.
Time that Nick would finish the marathon = 11.45 a.m.

Answer(s): (a) 11.15 a.m.; (b) 11.45 a.m.