Question 1148972
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            There is another way to solve the problem, using only one unknown.



<pre>
Let x be distance traveled by the taxi, in miles.

Then the walking distance is  (31-x) miles.


The time spent by the taxi is  {{{x/50}}}  hours.

The time walking is  {{{(31-x)/4}}}  hours.


The time equation is


    {{{(31-x)/4}}} + {{{x/50}}} = 2  hours.


To solve the equation, multiply both sides by 100.  You will get


    25*(31-x)   + 2x = 200

    25*31 - 25x + 2x = 200

    25*31 - 200      = 25x - 2x

    x           = {{{(25*31-200)/23}}} = 25 km.


<U>ANSWER</U>.  The distance to pay the cab driver for is  25 kilometers.


<U>CHECK</U>.   {{{(31-25)/4}}} + {{{25/50}}} = {{{6/4}}} + {{{1/2}}} = {{{3/2}}} + {{{1/2}}} = {{{4/2}}} = 2 hours.   ! Precisely correct !
</pre>

Solved.


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No one of the two methods is better than the other.


They both are good.


Which one to use, depends on your preferences and methods you use in the class.


But you will benefit, if you know BOTH methods.