dmf576476
Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Find the rate in miles per hour. 5 1/3 miles in 7 1/2 minutes

Sagot :

JonHenderson55

The answer is:  " [tex]42\frac{2}{3}[/tex] miles per hour " .

_______

Step-by-step explanation:

This is a "unit rate" problem.

"Find the rate in miles per "single [unit] hour."

 {GIven:  "5 1/3 mi per 7 1/2 min."}.

_______

Using a technique unknown as "dimension analysis" ;

let us convert the given value; in "mi / min" ;

 to its value in "mi/hr" (our answer):

_______

→    " 5 1/3  mi        60 min                  ,    

      ________  *   ______   =   ?      mi / hr ?  "

       7 1/2 min           1 hr

_______

Note:  The units of "min" ["minute(s)"] ; cancel out to "1" ;

               →  {since:  "min/min = 1 " ;

  and we have:  " [ (5  1/3 * 60) / (7 1/2) ] mi / hr. " ;

_______

   →   " 5  1/3 =  [ (3*5) + 1 ] / 3 " ;

                                  = " (15 + 1) /3 " ;

                                  = " 16 / 3 " ;  → (as an "improper fraction") ;

   →   " 7  1/2 =  [ (2*7) + 1 ] / 2 " ;

                                  =  " (14 + 1) / 2) " ;

                                  = "  15 / 2 " ;   → (as an "improper fraction") ;

_______

So we have:

   →   " [tex](\frac{16}{3}*\frac{60}{1})[/tex] ÷ [tex]\frac{15}{2}[/tex] " ;

Note: Dividing by a value is the same value as multiplying by the reciprocal of that value.

 In this case:  The reciprocal of:  " [tex](\frac{15}{2}[/tex][tex])[/tex] " ;  is:  " [tex](\frac{2}{15})[/tex] " ;

_______

So, we can rewrite the expression:

_______

   →   " [tex](\frac{16}{3}*\frac{60}{1}) * \frac{2}{15}[/tex] " ;

_______

     =  " [tex]\frac{(16*60*2)}{(3*1*15)}[/tex] " ;

   

 →   "    ( 16 * 60 * 2)      "

             (3 * 15)    

 →   Take note of the "60" in the numerator;  and the "15" in the denominator ;

  " (60 ÷ 15 = 4) " ;  

 so we can change the "60" to a "15" and cancel out the "15" ; since:

  " (15 ÷ 15 = 1 ) " ;  

_______

And rewrite:

_______

   →   "    ( 16 * 4 * 2)      "  

                    3       ;

_______

[tex]= \frac{(16 * 4 * 2)}{3} = \frac{(64*2)}{3} = \frac{128}{3} =[/tex]  (128 ÷ 3) =  " [tex]42\frac{2}{3}[/tex] " .

_______

The answer is:  " [tex]42\frac{2}{3}[/tex] miles per hour " .

_______

Hope this is helpful!

 Best of luck to you!

_______

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.