Question 1143969
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Let x be the Kirk' speed, in miles per hour.


Then the Spock' speed is (x+30) mph.


The time for Kirk is  {{{300/x}}} hours.


The time for Spock is  {{{240/(x+30)}}} mph.


The time equation is


    {{{300/x}}} = {{{2*(240/(x+30))}}}.


From this equation,


    300*(x+30) = 480x,

    300x + 9000 = 480x

    9000 = 480x - 300x

    9000 = 180x

    x = {{{9000/180}}} = 50.


<U>ANSWER</U>.  Kirk' speed is  50 mph;  Spock' speed is 50+30 = 80 mph.

                Kirk's time is  {{{300/50}}} = 6 hours;  Spock' speed is  {{{240/80}}} = 3 hours.
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Solved.