Question 1186764
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Cyclist A travelled 60 km. Cyclist B travels 5 km/hr faster than A 
and travels the same distance in 2 hours less. Find the speed of each.
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            The solution by @Alan is incorrect.

            I came to bring you a correct solution.



<pre>
Let x be the speed of cyclist A, in km/h.

Then the speed of cyclist B is (x+5) km/h, according to the condition.


Cyclist A spent  {{{60/x}}}      hours.

Cyclist B spent  {{{60/(x+5)}}}  hours.


The difference of times is 2 hours.   It gives you THIS "time equation"

    {{{60/x}}} - {{{60/(x+5)}}} = 2.      (1)



        At this point, I just can to guess the answer mentally :  it is  x= 10 km/h.

        But let's get it formally . . . 



From the time equation, by multiplying both sides by x*(x+5) you get

    60(x+5) - 60x = 2x*(x+5)

    60x + 300 - 60x = 2x^2 + 10x

          300       = 2x^2 + 10x

          2x^2 + 10x - 300 = 0

           x^2 +  5x - 150 = 0


Factor left side


           (x-10)*(x+15) = 0


The last equation has two roots,  10 and -15,  of which we select the positive value  x= 10.


<U>ANSWER</U>.  Cyclists A  speed is 10 km/h;  Cyclist B speed is 10+5 = 15 km/h.


<U>CHECK</U>.  Calculate left side of the equation (1).  It is  {{{60/10}}} - {{{60/15}}} = 6 - 4 = 2  hours.  ! Correct !
</pre>

Solved.


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Couple of words as a conclusion.


What I presented here, &nbsp;is a standard version and a standard way solving such problems using &nbsp;"time equation".


It is straightforward and clear. &nbsp;It prevents you of making mistakes.


If you deviate from this scheme of writing the solution, &nbsp;and will write a mess, &nbsp;then &nbsp;NOTHING &nbsp;will prevent you 

of making mistakes on the way.