Question 1142773
.


            When students solve such problems,  the major difficulty is to setup a governing equation.


            I will show you a standard and straightforward way to do it.



<pre>
Let r be the rate of train B, in kilometers per hour (the unknown value under the question).

Then the rate of the train A is  (r+10) km/h, according to the condition.



Train's  B  traveling time is  {{{100/r}}}  hours.

Train's  A  traveling time is  {{{100/(r+10)}}}  hours.



The difference of traveling times is  {{{1/2}}}  of an hour, according to the condition.



It gives you this "time" equation


    {{{100/r}}} - {{{100/(r+10)}}} = {{{1/2}}}  hours.           <<<---=== Every fraction on the left side is the traveling time . . .  



<U>At this point, the setup is just completed</U> (!)



To solve the equation, multiply both sides by 2*r*(r+10). You will get


    200*(r+10) - 200*r = r*(r+10)

    2000 = r^2 + 10r

    r^2 + 10r - 2000 = 0

    (r+50)*(r-40) = 0


The two roots of the equation are r = -50  and  r = 40,  but only positive r = 40 km/h makes sense and is the solution to the problem.


<U>ANSWER</U>. The rate of train B  is  40 kilometers per hour.


<U>CHECK</U>.   Travel time for train A is  {{{100/(40+10)}}} = {{{100/50}}} = 2 hours;  
 
         Travel time for train B is  {{{100/40}}} = {{{2}}}{{{1/2}}} hours, which is 30 minutes longer than that of train A.   ! Correct !
</pre>

Solved


Using "time" equation is the STANDARD way to solve such problems.


From this solution, &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;- <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.