Billy and Howard took part in a 16 km marathon. Billy 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. Howard ran half his total time at 12 km/h and ran slower for the rest of the time at 10 km/h. If they started the marathon at 4.30 a.m., at what time would each of them finish?

1. Billy
2. Howard

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

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 ÷ 8
= 1 h

Total time taken by Billy
= 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 4.30 a.m. = 6.18 a.m.
Time that Billy would finish the marathon = 6.18 a.m.

(b)
Time taken by Howard for the first half of the marathon
= 8 ÷ 12
= ²₃ h

Time taken by Howard for the last half of the marathon
= 8 ÷ 10
= ⁴₅ h

Total time taken by Howard
= ²₃ + ⁴₅
= 1⁷₁₅ h

1 h = 60 min
⁷₁₅ h = ⁷₁₅ x 60 = 28 min
1⁷₁₅ h = 1 h 28 min
1 h 28 min after 4.30 a.m. = 5.58 a.m.
Time that Howard would finish the marathon = 5.58 a.m.

Answer(s): (a) 6.18 a.m.; (b) 5.58 a.m.