Karen ran four and a half kilometers in 22 and a half minutes. How many minutes would it take her to run five kilometers if she ran at the same rate?
We are told in the question that Karen ran four and a half kilometers in 22 and a half minutes. Our first step is to calculate how long it would take Karen to run one kilometer at this rate. Four and a half divided by four and a half is equal to one. Whatever we do to the distance we must also do to the time. Therefore, we need to divide 22 and a half by four and a half. Four and a half is the same as 4.5, and 22 and a half is the same as 22.5.
We need to work out how many times 4.5 goes into 22.5. One multiplied by 4.5 is 4.5. Adding 4.5 repeatedly would give us the answers to two multiplied by 4.5, three multiplied by 4.5, and so on. Using this method, we can see that five multiplied by 4.5 is equal to 22.5. This means that 22 and a half divided by four and a half is equal to five. If Karen is running at the same rate, she would complete one kilometer in five minutes.
We were asked to work out how long it would take her to run five kilometers. One multiplied by five is equal to five. As we’ve multiplied the distance by five, we also need to multiply the time by five. Five multiplied by five is equal to 25. Therefore, Karen would run five kilometers in 25 minutes.
We can check if this answer is sensible by comparing it to our original time. She ran four and a half kilometers in 22 and a half minutes. Therefore, she will run five kilometers in a slightly longer time. 25 minutes is slightly longer than 22 and a half minutes.