Warren and Billy took part in a 16 km marathon. Warren ran half the distance at a speed of 10 km/h and ran slower for the rest of the way at a speed of 8 km/h. Billy ran half his total time at 10 km/h and ran slower for the rest of the time at 6 km/h. If they started the marathon at 3.30 a.m., at what time would each of them finish?

1. Warren
2. Billy

(a)
Half of the 16 km marathon = 16 ÷ 2 = 8 km

Time taken by Warren for the first half of the marathon
= 8 ÷ 10
= ⁴₅ h

Time taken by Warren for the last half of the marathon
= 8 ÷ 8
= 1 h

Total time taken by Warren
= ⁴₅ + 1
= 1⁴₅ h

1 h = 60 min
⁴₅ h = ⁴₅ x 60 = 48 min
1⁴₅ h = 1 h 48 min

1 h 48 min after 3.30 a.m. = 5.18 a.m.
Time that Warren would finish the marathon = 5.18 a.m.

(b)
Time taken by Billy for the first half of the marathon
= 8 ÷ 10
= ⁴₅ h

Time taken by Billy for the last half of the marathon
= 8 ÷ 6
= 1¹₃ h

Total time taken by Billy
= ⁴₅ + 1¹₃
= 2²₁₅ h

1 h = 60 min
²₁₅ h = ²₁₅ x 60 = 8 min
2²₁₅ h = 2 h 8 min
2 h 8 min after 3.30 a.m. = 5.38 a.m.
Time that Billy would finish the marathon = 5.38 a.m.

Answer(s): (a) 5.18 a.m.; (b) 5.38 a.m.