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Ms. Johnson’s running shoes need to be replaced every 500 km. Each year, she runs from April to October for 30 consecutive weeks, 4 days a week, 7 km a day.
(a) If she buys new shoes before her first run of the year, how many weeks will it be until her shoes need to be replaced?
(b) How many times will she need to replace her shoes in one year?
(a) Since Ms. Johnson runs 4 days a week and 7 km a day, in one week she runs 4 × 7 = 28 km.
We need to find out how many weeks it takes to run 500 km. We can divide 500 by 28:
500 ÷ 28 ≈ 17.86
This means that after 17 full weeks, she will have run 17 × 28 = 476 km, and during the 18th week, she will exceed 500 km.
So, she will need to replace her shoes after 18 weeks.
(b) From part (a), we know that her shoes need to be replaced every 18 weeks.
In 30 weeks:
Counting the new pair at the start of the year, Ms. Johnson will need to replace her shoes 2 times in one year.