Question 1157345
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>The way how the beginner student solves such problems</U>


<pre>
Let t be the time, in hours, before the trains will meet each other.


At that time, Train A will cover 30*t kilometers;

              train B will cover 45*t kilometers.

The distances they cover sum up the whole distance of 300 kilometers.


It gives you an equation

    30*t + 45*t = 300   kilometers,   or

    (30+45)*t = 300,

    75t       = 300

      t       = {{{300/75}}} = 4 hours.


Then the distance from A is  30*4 = 120 kilometers.


<U>ANSWER</U>.  They will meet each other in 4 hours.
</pre>

Solved.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>The way for more advanced students</U>.


<pre>
Let d be the distance from A (the unknown under the question).

Then the distance from B is  300-d  kilometers.


The time spent by A-train is  {{{d/30}}} hours.

The time spent by B-train is  {{{d/45}}} hours.


The time is the same, which gives you an equation

    {{{d/30}}} = {{{(300-d)/45}}}.


Multiply both sides by 90.

    3d = 2*(300-d),   or

    3d = 600 - 2d

    3d + 2d = 600

    5d      = 600

     d      = {{{600/5}}} = 120 kilometers.


You got the same answer (!)
</pre>

Solved.


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See introductory lessons on Travel and Distance problems

&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>

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Hey,

who is a composer/(problems writer) on your side ?


Tell him (or her), &nbsp;by referring to me, &nbsp;that he &nbsp;(or she) &nbsp;does his &nbsp;(or her) &nbsp;job by &nbsp;NOT &nbsp;in a &nbsp;PERFECT &nbsp;mode.


The correct condition must sound in this way:


<pre>
    Points A and B are 300 km apart. A train travels from A to B at 30 km per hour and another train travels 
    from B to A at 45 km per hour. At what distance from A will both trains meet each other, if they depart simultaneously ?
</pre>