Max and Angela are both long-distance runners, but Angela runs more than Max. For every hour that Max spends running, Angela spends an hour and a half. Write a ratio that compares the time that Max spends running to the time that Angela spends running.
Answer (1)
Define M as Max's running time and A as Angela's running time.
Express the relationship: A = 1.5 M .
Write the ratio of Max's time to Angela's time as M : A = M : 1.5 M , which simplifies to 1 : 1.5 .
Multiply by 2 to remove the decimal, resulting in the ratio 3 2 .
Explanation
Understanding the Problem Let's analyze the problem. We are given that Angela runs more than Max, and for every hour Max spends running, Angela spends an hour and a half. We need to find the ratio of the time Max spends running to the time Angela spends running.
Defining Variables Let M be the time Max spends running and A be the time Angela spends running. We are given that A = 1.5M. We want to find the ratio M:A.
Expressing the Ratio Since A = 1.5M, the ratio M:A can be written as M:1.5M. To simplify this ratio, we can divide both sides by M, which gives us 1:1.5.
Simplifying the Ratio To get rid of the decimal, we can multiply both sides of the ratio 1:1.5 by 2. This gives us 2:3. Therefore, the ratio of the time Max spends running to the time Angela spends running is 2:3, which can also be written as 3 2 .
Examples
Ratios are used in everyday life to compare quantities. For example, if you are baking a cake and the recipe calls for a ratio of 2 cups of flour to 1 cup of sugar, this means that for every 1 cup of sugar, you need 2 cups of flour. Understanding ratios helps you scale recipes, mix paint colors, or even understand financial statements. In this case, the ratio of Max's running time to Angela's running time helps us understand how their running times compare. If Max runs for 2 hours, Angela runs for 3 hours.
