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]$D=5 h+3$[/tex]
B. [tex]$D=3 h+5$[/tex]
C. [tex]$D=3 h-5$[/tex]
D. [tex]$D=3(h-5)$[/tex]
Answer (2)
Sarah already traveled 5 miles.
She travels an additional 3 h miles after the break.
The total distance is the sum of these two distances: D = 3 h + 5 .
The correct answer is B: D = 3 h + 5 .
Explanation
Problem Analysis Let's analyze the problem. Sarah has 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 Calculation The distance Sarah traveled before the break is a constant 5 miles. The distance she travels after the break is her speed (3 miles per hour) multiplied by the time she hikes ( h hours), which is 3 h . The total distance D is the sum of these two distances.
Equation Formulation Therefore, the equation that models the total distance is: D = 5 + 3 h This can also be written as: D = 3 h + 5
Selecting the Correct Option Now, let's compare this equation with the given options: A. D = 5 h + 3 B. D = 3 h + 5 C. D = 3 h − 5 D. D = 3 ( h − 5 )
The correct equation is D = 3 h + 5 , which matches option B.
Examples
Imagine you're tracking your progress on a fitness challenge. You've already walked 5 miles this week, and you plan to walk 3 miles each additional day. The equation D = 3 h + 5 helps you calculate your total distance D after h days. This kind of equation is useful for planning and tracking progress in various real-life situations, from fitness goals to project management.
The equation that models the total distance Sarah travels after hiking for an additional h hours is D = 3 h + 5 , which corresponds to option B. This reflects the initial 5 miles she covered plus the additional distance traveled at 3 miles per hour for h hours. Therefore, the correct answer is B: D = 3 h + 5 .
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