Select the correct answer.

Sarah is hiking on a trail near her home. She traveled 5 miles before stopping for a break. After the break, Sarah plans on increasing her speed to 3 miles per hour. Which equation models the total distance, [tex]$D$[/tex], Sarah travels after hiking for an additional [tex]$h$[/tex] hours?
A. [tex]$D=3 h-5$[/tex]
B. [tex]$D=5 h+3$[/tex]
C. [tex]$D=3(h-5)$[/tex]
D. [tex]$D=3 h+5$[/tex]

Question

Select the correct answer.

Sarah is hiking on a trail near her home. She traveled 5 miles before stopping for a break. After the break, Sarah plans on increasing her speed to 3 miles per hour. Which equation models the total distance, [tex]$D$[/tex], Sarah travels after hiking for an additional [tex]$h$[/tex] hours?
A. [tex]$D=3 h-5$[/tex]
B. [tex]$D=5 h+3$[/tex]
C. [tex]$D=3(h-5)$[/tex]
D. [tex]$D=3 h+5$[/tex]

GinnyAnswer · Answer

Sarah starts with 5 miles. 
 She then hikes at 3 miles per hour for h hours, covering 3 h miles. 
 The total distance D is the sum of these two distances. 
 Therefore, the equation is D = 3 h + 5 ​ . 
 
 Explanation 
 
 Problem Analysis Let's analyze the problem. Sarah already hiked 5 miles. After her break, she hikes at a speed of 3 miles per hour for an additional h hours. We need to find the equation that represents the total distance D she travels. 
 
 Distance After the Break The distance Sarah travels after the break is her speed multiplied by the time she hikes, which is 3 × h = 3 h miles. 
 
 Total Distance The total distance D is the sum of the distance she traveled before the break (5 miles) and the distance she travels after the break ( 3 h miles). Therefore, the equation is D = 3 h + 5 . 
 
 Finding the Correct Option Comparing this equation with the given options, we see that option D, D = 3 h + 5 , matches our result.

Examples 
 Imagine you're tracking the progress of a long-distance runner. They've already run 10 miles, and now they're maintaining a pace of 6 miles per hour. This problem helps you calculate their total distance at any given time. Understanding how to model such scenarios allows you to predict arrival times, manage resources, and make informed decisions based on real-time data. This is useful in logistics, sports analytics, and even everyday planning.

Anonymous · Answer

Sarah's total distance traveled can be represented by the equation D = 3 h + 5 , where h is the additional time she hikes after her break. This is derived from her initial hike of 5 miles and her subsequent pace of 3 miles per hour. Thus, the correct answer is D. 
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Answer (2)

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