Q:

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

Accepted Solution

A:

A . D=3h+5     
Let's look at the problem and break it down into an equation.  
"She traveled 5 miles before stopping for a break ."  
This indicates that we have the constant 5 in the equation without any other modifiers. So let's start off with:  
5    
"After the break , Sarah plans on increasing her spied to 3 miles per hour"  
OK. We now know that she'll be traveling at 3 mph. So let's keep that "3 mph" in mind.    
"Which equation models the total distance ,D, Sarah travels after hiking for an additional h hours"  
We now know that Sarah will be traveling for an additional h hours. And since the previous statement told us that she would be traveling at 3 mph, that means that we can add 3h to the number of miles that she's already traveled.
So we have a good equation of:  
D = 5 + 3h    
Looking at the available options, only "A" matches. Even though "A" isn't initially an exact match, you can make it an exact match by using the commutative property of addition to change our equation to match it.
Because of that, the correct answer is "A".