Question 874687
CONDITION________speed________time_______distance
Did_______________x____________t_________{{{120=xt}}}
If_______________x+1__________t-1/2______{{{120=(x+2)(t-1/2)}}}


Both x and t can be solved.  See that a substitution will be possible using the "did" equation.


The "If" equation,
{{{xt+2t-x/2-1=120}}}
{{{xt+2t-x/2-1=xt}}}
{{{2t-x/2-1=0}}}
{{{4t-x-2=0}}}
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Again substitute using {{{t=120/x}}}.
{{{480/x-x-2=0}}}
{{{480-x^2-2x=0}}}
{{{-x^2-2x+480=0}}}
{{{highlight(x^2+2x-480=0)}}}.
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Check discriminant.  4+4*480=1924.
481 is a prime number.
4(481) is discriminant.
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{{{x=(-2+sqrt(4*481))/2}}}
{{{x=(-2+2sqrt(481))/2}}}
{{{highlight(x=-1+sqrt(481))}}}