Question

Enter the missing numbers in the boxes to complete the table of equivalent ratios of time to distance.

Answer 1

Answer:  Here is the complete table, with the filled in values:
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Time (h)    Distance (mi)
    3                2 
    9                6
   12                8
   18               12
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Explanation:
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Let us begin by obtaining the "?" value; that is, the "distance" (in "mi.") ;
         when the time (in "h") is "18" ; 
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12/8 = 18/?  

Note: "12/8 = (12÷4) / (8÷4) = 3/2 ;

Rewrite:  3/2 = 18/? ;  cross-multiply:  3*? = 2 * 18 ; 
                                                                        3*? = 36 ;

                                                                      Divide each side by "3" ;
                                                                            The "?" = 36/3 = 12 ;

So, 12/8 = 18/12 ;

The value: "12" takes the place for the "?" in the table for "distance (in "mi.);
                              when the "time" (in "h") is "18".
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Now, let us obtain the "? " value for the "distance" (in "mi.");
                when the "time" (in "h") is:  "9" .

12/8 = 9/? ;  Solve for "?" ;

We know (see aforementioned) that "12/8 = 3/2" ; 

So, we can rewrite:  3/2 = 9/? ;  Solve for "?" ; 

Cross-multiply:  3* ? = 2* 9 ;    3* ? = 18 ;  
                                                           Divide each side by "3" ;
                                                    to  get:  "6" for the "?" value.

When the time (in "h") is "9", the distance (in "mi.") is "6" .
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Now, to solve the final "?" value in the table given.

9/6 = ?/2 ;  Note:  We get the "6" from our "calculated value" (see above problem). 

9/6 = (9÷3) / (6÷3) = 3/2 ;  

So, we know that the "?" value is:  "3" .

Alternately:   9/6 = ?/2 ; 

Cross-multiply:  6*? = 2*9 ;   6 * ? = 18 ;  Divide each side by "6" ;
                                                               to find the value for the "?" ; 
                                                                    "?" = 18/6 = "3" .

When the "distance" (in "mi.") is:  "2" ;  the time (in "h") is:  "3" .
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Here is the complete table—with all the values filled in:
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Time (h)    Distance (mi)
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    3                2 
    9                6
   12                8
   18               12
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