Question 27418
you mis-quoted the formula... it is {{{T= To/sqrt(1-(v/c)^2)}}}


Re-arranging, first get rid of the square root by squaring both sides, giving


{{{T^2 = To^2/(1-(v/c)^2)}}}
{{{1-(v/c)^2 = (To^2)/(T^2)}}}
{{{1 - ((To^2)/(T^2)) = (v/c)^2}}}
{{{sqrt(1 - ((To^2)/(T^2))) = v/c}}}
{{{c*sqrt(1 - ((To^2)/(T^2))) = v}}}


Now, this is an answer. You could also mess with the square root term and combine the 1 to the fraction. Ultimately you will get:


{{{v = (c*sqrt((T-To)(T+To)))/T }}}


So, 
T = 8 hrs
To = 4 hrs
c = 186,000 miles per second


First thing... convert all terms to consistent units: you have times in hours yet your speed of light is miles per SECOND.


I shall convert the speed to miles per hour:


186,000 miles EVERY second is
186,000*60 miles EVERY minute ---> you will go further in a minute than a second
186,000*60*60 miles EVERY hour ---> you will go further in an hour than a minute


So, put the numbers into the formula, giving: {{{v=c*sqrt(1 - ((To^2)/(T^2)))}}}
{{{v=(18600*60*60)*sqrt(1 - ((4^2)/(8^2)))}}}
{{{v=(18600*3600)*sqrt(1 - ((16)/(64)))}}}
{{{v=(18600*3600)*sqrt(1 - (1/4)) }}}
{{{v=(18600*3600)*sqrt(3/4) }}}


now use a calculator... v = 3350 miles per hour


jon.