Billy and Xavier 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 5 km/h. Xavier ran half his total time at 12 km/h and ran slower for the rest of the time at 5 km/h. If they started the marathon at 5.30 a.m., at what time would each of them finish?

1. Billy
2. Xavier

(a)
Half of the 24 km marathon = 24 ÷ 2 = 12 km

Time taken by Billy for the first half of the marathon
= 12 ÷ 9
= 1¹₃ h

Time taken by Billy for the last half of the marathon
= 12 ÷ 5
= 2²₅ h

Total time taken by Billy
= 1¹₃ + 2²₅
= 3¹¹₁₅ h

1 h = 60 min
¹¹₁₅ h = ¹¹₁₅ x 60 = 44 min
3¹¹₁₅ h = 3 h 44 min

3 h 44 min after 5.30 a.m. = 9.14 a.m.
Time that Billy would finish the marathon = 9.14 a.m.

(b)
Time taken by Xavier for the first half of the marathon
= 12 ÷ 12
= 1 h

Time taken by Xavier for the last half of the marathon
= 12 ÷ 5
= 2²₅ h

Total time taken by Xavier
= 1 + 2²₅
= 3²₅ h

1 h = 60 min
²₅ h = ²₅ x 60 = 24 min
3²₅ h = 3 h 24 min
3 h 24 min after 5.30 a.m. = 8.54 a.m.
Time that Xavier would finish the marathon = 8.54 a.m.

Answer(s): (a) 9.14 a.m.; (b) 8.54 a.m.