Some of the students at Georgia Middle School like to walk to and from school. They always walk unless it rains. Let d be the distance in miles from a student's home to the school. Write two different expressions that represent how far a student travels by walking in a two week period if there is one rainy day each week.
Expression 1: 2d - This expression represents the distance a student travels by walking in a two-week period if there is one rainy day each week. In each week, the student walks d miles to school and d miles back home. Since there are two weeks, the student walks a total of 2d miles.
Expression 2: 4d - This expression also represents the distance a student travels by walking in a two-week period if there is one rainy day each week. In this expression, the student walks d miles to school and d miles back home in the first week. Then, in the second week, they walk d miles to school and d miles back home again. Therefore, the student walks a total of 4d miles in two weeks.
can you show me the entire working process, please?
Sure! Let's break it down step by step:
Step 1: Determine the distance a student travels by walking in one week if there is one rainy day.
In one week, a student walks d miles to school and d miles back home. Since there is one rainy day each week, the student will not be walking on that day. Therefore, the student walks a total of (d + d - 0) = 2d miles in one week.
Step 2: Determine the distance a student travels by walking in a two-week period if there is one rainy day each week.
Since the student walks 2d miles in one week, they will walk the same distance in the second week as well. Therefore, in a two-week period with one rainy day each week, the student will walk a total of (2d + 2d) = 4d miles.