Question 1092475
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<U>Solution 1</U>  &nbsp;&nbsp;&nbsp;&nbsp;(for beginners)


<pre>
Let t be the time under the question, in hours.

Then the first   plane will cover the distance  450*t miles in t hour,
while the second plane will cover the distance  550*t miles in t hour.


Since they fly in opposite directions, the distance between them in t hours will be 

450*t + 550*t.


According to the condition, the distance is 4000 miles. It gives an equation

450*t + 550*t = 4000.

Simplify and solve for t:

(450+550)*t = 4000 ====>  1000*t = 4000  ====>  t = {{{4000/1000}}} = 4 hours.


<U>Answer</U>.  It will take 4 hours.
</pre>


<U>Solution 2</U>  &nbsp;&nbsp;&nbsp;&nbsp;(for more advanced students)


<pre>
Since their relative speed is 450 km/h + 550 km/h, the distance between the planes increases at the rate (450 + 550) = 1000 km/h.


Now apply the formula  t = {{{Distance/Rate}}} = {{{4000/1000}}} = 4 hours.


You get the same answer.
</pre>


See the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Travel-and-Distance-problems.lesson>Travel and Distance problems</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Travel-and-Distance-problems-for-two-bodies-moving-toward-each-other.lesson>Travel and Distance problems for two bodies moving in opposite directions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Typical-catching-up-Travel-and-Distance-problems.lesson>Travel and Distance problems for two bodies moving in the same direction (catching up)</A>

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the section "<U>Word problems</U>", &nbsp;the topic "<U>Travel and Distance problems</U>".