Liam was training for a swimming competition. On Day 1 of his training, he swam 500 m. On Day 2, he swam 1.5 km more than Day 1. For each subsequent training session, he swam a distance of 1.5 km more than the previous training session.
- On Day 9 of his training session, how far did he swim? Give your answer in km.
- On which day did he swim a distance of 5 km?
(a)
1000 m = 1 km
500 m = 0.5 km
Pattern for the distance swam
Day 1: ((1 - 1) x 1.5) + 0.5 = 0.5
Day 2: ((2 - 1) x 1.5) + 0.5 = 2
Day 3: ((3 - 1) x 1.5) + 0.5 = 3.5
Formula
Distance swam = ((Number of day - 1) x 1.5) + 0.5
Distance swam on Day 9
= [(9 - 1) x 1.5] + 0.5
= 8 x 1.5 + 0.5
= 12 + 0.5
= 12.5 km
(b)
Number of days he swam 5 km
= [(5 - 0.5) ÷ 1.5] + 1
= 4.5 ÷ 1.5 + 1
= 3 + 1
= 4
Answer(s): (a) 12.5 km; (b) 4