Question 1148210
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<pre>

Based on the given data, I can guess the answer in 5 seconds.


    His running speed is 5 miles per hour.


<U>CHECK</U>.  He spent 1 hour running and {{{80/(5+15)}}} = 4 hours biking.
</pre>


But if you want ALGEBRA solution, here it is.



<pre>
Let x be the running speed, which is the value under the question.

Then his biking speed is  (x+15) miles per hour.


The time spent running is  {{{5/x}}}  hours.

The time spent biking is  {{{80/(x+15)}}}.


The total time is 5 hours; it gives you and equation


    {{{5/x}}} + {{{80/(x+15)}}} = 5   hours.


It is so called "time" equation.

As soon as you got it, the setup is just completed.

Now your task is to solve it.


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


    5*(x+15) + 80x = 5x*(x+15)

    (x+15)   + 16x = x*(x+15)

    17x + 15       = x^2 + 15x

     x^2 - 2x - 15 = 0

     (x-5)*(x+3)    = 0


Of the two roots, x= 5  and  x= -3, only positive x= 5 makes sense.


So, your answer is:  the running speed is  5 mph;  same as I guessed at the beginning.
</pre>

Solved.


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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

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