David was training for a swimming competition. On Day 1 of his training, he swam 500 m. On Day 2, he swam 0.5 km more than Day 1. For each subsequent training session, he swam a distance of 0.5 km more than the previous training session.
- On Day 7 of his training session, how far did he swim? Give your answer in km.
- On which day did he swim a distance of 3 km?
(a)
1000 m = 1 km
500 m = 0.5 km
Pattern for the distance swam
Day 1: ((1 - 1) x 0.5) + 0.5 = 0.5
Day 2: ((2 - 1) x 0.5) + 0.5 = 1
Day 3: ((3 - 1) x 0.5) + 0.5 = 1.5
Formula
Distance swam = ((Number of day - 1) x 0.5) + 0.5
Distance swam on Day 7
= [(7 - 1) x 0.5] + 0.5
= 6 x 0.5 + 0.5
= 3 + 0.5
= 3.5 km
(b)
Number of days he swam 3 km
= [(3 - 0.5) ÷ 0.5] + 1
= 2.5 ÷ 0.5 + 1
= 5 + 1
= 6
Answer(s): (a) 3.5 km; (b) 6