Question

a group of students in a health class track their daily steps to find out how far they walk. the students use different smartphone apps to track their distances. some apps display distances using decimals while others use fractions. the table shows the total distances walked by the group of students so far. the battery of shaunas phone ran out of power before her distance could be recorded. answer the question below. click the icon to view the table of distances walked. shauna knows that she walked farther than todd, but not as far as jin. mariko predicts that the total distance the group walked is between 60 and 65 miles. how might mariko have determined this? there are 5 students and each student walked more than miles, so the total must be greater than ×5 = 60. each student walked fewer than miles, so the total must be less than ×5 = 65.

Explanation:

Step1: Find lower - bound per - student distance

We know that the total lower - bound of the group distance is 60 miles and there are 5 students. To find the lower - bound per - student distance, we use the formula for total distance \(T = n\times d\) (where \(T\) is total distance, \(n\) is number of students, and \(d\) is distance per student). Rearranging for \(d\) gives \(d=\frac{T}{n}\). So, \(d = \frac{60}{5}=12\) miles.

Step2: Find upper - bound per - student distance

We know that the total upper - bound of the group distance is 65 miles and there are 5 students. Using the same formula \(T = n\times d\) and rearranging for \(d\), we get \(d=\frac{65}{5}=13\) miles.

Answer:

There are 5 students and each student walked more than 12 miles, so the total must be greater than 12×5 = 60. Each student walked fewer than 13 miles, so the total must be less than 13×5 = 65.