Xavier and Riordan took part in a 42 km marathon. Xavier ran half the distance at a speed of 12 km/h and ran slower for the rest of the way at a speed of 5 km/h. Riordan 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 5.30 a.m., at what time would each of them finish?

1. Xavier
2. Riordan

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

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

Time taken by Xavier for the last half of the marathon
= 21 ÷ 5
= 4¹₅ h

Total time taken by Xavier
= 1³₄ + 4¹₅
= 5¹⁹₂₀ h

1 h = 60 min
¹⁹₂₀ h = ¹⁹₂₀ x 60 = 57 min
5¹⁹₂₀ h = 5 h 57 min

5 h 57 min after 5.30 a.m. = 11.27 a.m.
Time that Xavier would finish the marathon = 11.27 a.m.

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

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

Total time taken by Riordan
= 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 5.30 a.m. = 10.45 a.m.
Time that Riordan would finish the marathon = 10.45 a.m.

Answer(s): (a) 11.27 a.m.; (b) 10.45 a.m.