Question 1144343
.


            Pay attention on how I edited your post to make wording correct.


<pre>
                A motorcycle driver travels 15 kph faster than a bicycle rider. 
                The motorcycle driver takes 2 hours less to cover 60 km than it takes the bicycle rider 
                to travel the same distance. What is the mathematical sentence
</pre>

<U>Solution</U>


<pre>
Let x be the bicycle average rate, in km/h.


Then the motorcycle average rate is (x+15) km/h, according to the condition.


The bicycle takes {{{60/x}} hours to cover 60 kilometers.

The motorcycle takes  {{{60/(x+15)}}} hours to cover the same distance.


The difference of times is 2 hours, as the condition states:


    {{{60/x}}} - {{{60/(x+15)}}} = 2   hours.


It is so called "time equation" -- the BASIC equation for such type of problems.


It is the equation -- "the mathematical sentence" -- you asked for.


To solve it, multiply both sides by x*(x+15). You will get


    60*(x+15) - 60x = 2x*(x+15).


Simplify and solve for x


     900 = 2x^2 + 30x

     2x^2 + 30x - 900 = 0

     x^2  + 15x - 450 = 0

     (x+30)*(x-15) = 0.


The roots are -30 and 15, but only positive x= 15 makes sense.


So, you get the <U>ANSWER</U>:  the bicycle average rate is 15 km/h;  the motorcycle average rate is 15+15 = 30 km/h.


<U>CHECK</U>.  {{{60/15}}} = 4 hour for the bicycle and  {{{60/30}}} = 2 hours for the motorcycle with the difference 4-2 = 2 hours.   ! Correct !
</pre>

Explained and solved.


----------------


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

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;- <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.