Question 1128494
.
<pre>
Let x be the car average speed.

The&#1090; the time for the trip is {{{560/x}}} hours.


Had the car moved 10 mph faster, its speed would be (x+10) mph and the time for the trip would be {{{560/(x+10)}}} hours.


The condition says that


    {{{560/x}}} - {{{560/(x+10)}}} = 1  hour.     (1)


The number 560 has two remarcable divisors 70 and 80 that differ by 10.

It gives me an idea that x= 70.


<U>Check</U>.  {{{560/70}}} - {{{560/80}}} = 8 - 7 = 1.


So, the answer is:  the car' speed under the question is  70 mph.


Surely, it is my guess ( ! the correct and checked guess, though !).


But you can solve the equation (1) algebraically, too.


For it, multiply both its sides by  x*(x+10).

You will get a quadratic equation


   560*(x+10) - 560x = x*(x+10),

    x^2 + 10x - 5600 = 0.


Factor the left side polynomial


    (x-70)*(x+80) = 0.


Only positive root  x= 70  is meaningful.


Thus we completed the algebraic solution, and got THE SAME answer:  the averaged speed of the car is 70 miles per hour.
</pre>


Solved.


Is everything clear to you in my post ?


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


You may find other similar solved problems in the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Selected-Travel-and-Distance-problems-from-the-archive.lesson>Selected Travel and Distance problems from the archive</A> 

&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>

in this site.