Question 1143050
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<pre>
Let d be the distance between the two airports (in miles).


Flying at the speed of  540 mph, the airplane spends  {{{d/540}}}  hours and arrives 8 minutes later.


Flying at the speed of  480 mph, the airplane spends  {{{d/480}}}  hours and arrives 53 minutes later.


The difference of times is  {{{d/480}}} - {{{d/540}}} hours.


From the other side, this difference is 53-8 = 45 minutes = {{{45/60}}} of an hour = {{{3/4}}}  of an hour.



It gives you the "time" equation


    {{{d/480}}} - {{{d/540}}} = {{{3/4}}}.


At this point, the setup is just completed.


To find "d", multiply both sides of the equation (1)  by 60.  You will get


    {{{d/8}}} - {{{d/9}}} = 45.


One more time, multiply both sides of the last equation by 72.  You will get


    9d - 8d = 72*45,

     d      = 3240


<U>ANSWER</U>.  The distance between the two airports is  3240 miles.


<U>CHECK</U>.   {{{3240/480}}} = 6.75 hours;    

         {{{3240/480}}} = 6 hours.

         The difference is 0.75 of an hour = {{{3/4}}} of an hour -- ! Correct !
</pre>

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Using &nbsp;"time" &nbsp;equation is the &nbsp;STANDARD &nbsp;method of solving such problems.


It is simple, &nbsp;logical, &nbsp;straightforward and economic. &nbsp;Going in this way, &nbsp;you will not make a mistake - the logic of the method 
prevents you of making mistakes.


From this lesson, &nbsp;learn on how to write, &nbsp;how to use and how to solve a &nbsp;"time" &nbsp;equation.


To see many other similar solved problems, &nbsp;look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Had-a-car-move-faster-it-would-arrive-quicker.lesson>Had a car move faster it would arrive sooner</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/How-far-do-you-live-from-school.lesson>How far do you live from school?</A> &nbsp;&nbsp;&nbsp;(*)

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Earthquake-waves.lesson>Earthquake waves</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Time-equation-HOW-TO-write-it-and-how-to-solve-it.lesson>Time equation: HOW TO use, HOW TO write and HOW TO solve it</A> 

in this site.



For the TWIN problem, &nbsp;see the lesson &nbsp;(*) &nbsp;in the list.