John and Eric took part in a 42 km marathon. John 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. Eric 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?

1. John
2. Eric

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

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

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

Total time taken by John
= 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 John would finish the marathon = 11.15 a.m.

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

Time taken by Eric for the last half of the marathon
= 21 ÷ 9
= 2¹₃ h

Total time taken by Eric
= 1³₄ + 2¹₃
= 4¹₁₂ h

1 h = 60 min
¹₁₂ h = ¹₁₂ x 60 = 5 min
4¹₁₂ h = 4 h 5 min
4 h 5 min after 6.30 a.m. = 10.35 a.m.
Time that Eric would finish the marathon = 10.35 a.m.

Answer(s): (a) 11.15 a.m.; (b) 10.35 a.m.