Question 480042
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If I want to pass a car just in front of me going at 55mph, what will my speed be to pass 
within 1/4 of a mile? Show me the mathematical work thanks.
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        As the problem is worded and presented in the post,  it is incomplete, unrealistic and non-sensical.


        To be complete and fully correct,  the problem should also provide the length of your car,

        and the lengths of the gaps between the cars when you start passing and when you complete passing.


        So, I will assume that the length of your car is 10 ft and both gaps between the cars

        are 50 ft, before and after passing.



<pre>
So, during the time of passing, another car should cover the distance 

    1/4 of a mile  {{{highlight(highlight(MINUS))}}}  (50 + 50 + 10) ft = {{{(1/4)*5280 - 110}}} = 1210 ft.


The speed of the other car is 

    55 miles per hour = {{{(55*5280)/3600}}} = 80.66667 feet per second (ft/s)   (rounded).


The time for the other car to cover 1210 ft is

    {{{1210/80.66667}}} = 15 seconds.


Your car should cover 1/4 miles, or  {{{(1/4)*5280)}}} = 1320 ft.   <<<---===  <U>It is how I read "to pass within 1/4 of a mile"</U>


Hence, your speed should be  

    {{{1320/15}}} = 88 feet per second,  or  {{{(88*3600)/5280}}} = 60 miles per hour.


<U>ANSWER</U>.  Your speed should be 60 miles per hour.
</pre>

Solved.