Question 435264
The 1st sentence says that Ed's speed is 25 miles/hr
faster than Frank's
Let {{{s}}} = Frank's speed
Let {{{t}}} = Ed's time to go 75 miles in his car
Frank's equation:
{{{ 75 = s*(t + 1.5) }}}
Ed's equation:
{{{ 75 = (s + 25)*t }}}
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This is 2 equations with 2 uhnknowns,
so it's solvable
Since the distances are equal,
{{{ s*(t + 1.5) = (s + 25)*t }}}
{{{ s*t + 1.5s = s*t + 25t }}}
{{{ 1.5s = 25t }}}
{{{ t = .06s }}}
{{{ 75 = s*(.06s + 1.5) }}}
{{{ 75 = .06s^2 + 1.5s }}}
{{{ 6s^2 + 150s - 7500 = 0 }}}
{{{ 2s^2 + 50s - 2500 = 0 }}}
Using quadratic formula:
{{{s = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 2}}}
{{{b = 50}}}
{{{c = -2500}}}
{{{s = (-50 +- sqrt( 50^2-4*2*(-2500) ))/(2*2) }}}
{{{s = (-50 +- sqrt( 2500 + 20000 )) / 4 }}}
{{{ s = ( -50 + 150 )/4 }}}
{{{ s = 100/4 }}}
{{{ s = 25 }}}
Frank's speed is 25 mi/hr
check answer:
{{{ 75 = s*(t + 1.5) }}}
{{{ 75 = 25*(t + 1.5) }}}
{{{ 75 = 25t + 37.5 }}}
{{{ 25t = 37.5 }}}
{{{ t = 1.5 }}} hr
OK
{{{ 75 = (s + 25)*t }}}
{{{ 75 = (25 + 25)*t }}}
{{{ 75 = 50t }}}
{{{ t = 1.5 }}}
OK