Question 528170
Let {{{ w }}} = rate walking
Let {{{ b }}} = rate biking
given:
{{{ b = w + 10 }}} mi/hr
{{{ t[w] + t[b] =5 }}} hrs
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biking:
{{{ 12 = ( w + 10 )*t[b] }}}
walking:
{{{ 8 = w*t[w] }}}
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By substitution:
{{{ t[b] = 5 - t[w] }}}
{{{ 12 = ( w + 10 )*( 5 - t[w] ) }}}
{{{ 12 = 5w + 50 - w*t[w] - 10t[w] }}}
By substitution again:
{{{ 12 = 5w + 50 - 8 - 10t[w] }}}
Substitution again:
{{{ 12 = 5w + 50 - 8 - 10*(8/w) }}}
{{{ 80/w - 5w = 30 }}}
{{{ 80 - 5w^2  = 30w }}}
{{{ w^2 + 6w = 16 }}}
Completing the square:
{{{ w^2 + 6w + (6/2)^2 = 16 + (6/2)^2 }}}
{{{ w^2 + 6w + 9 = 16 + 9 }}}
{{{ ( w + 3 )^2 = 25 }}}
{{{ w + 3 = 5 }}}
{{{ w = 2 }}} ( can't use the negative root )
and
{{{ b = w + 10 }}}
{{{ b = 12 }}}
His speed biking was 12 mi/hr
His speed walking was 2 mi/hr