Question 775609
Let {{{ t }}} = the time in hours for his trip
if he is to arrive at the scheduled time
Let {{{ d }}} = distance from school to house in km
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Equation for leaving early:
{{{ d = 4*( t  - 10/60 ) }}}
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Equation for leaving late:
{{{ d = 3*( t + 10/60 ) }}}
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By substitution:
{{{ 4*( t - 1/6 ) = 3*( t + 1/6 ) }}}
{{{ 4t - 2/3 = 3t + 1/2 }}}
{{{ t = 1/2 + 2/3 }}}
Multiply both sides by {{{ 6 }}}
{{{ 6t = 3 + 4 }}}
{{{ t = 7/6 }}} 
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By substitution:
{{{ d = 4*( 70/60 - 10/60 ) }}}
{{{ d = 4 }}} km
The distance of the school from his house is 4 km
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check:
{{{ d = 3*( t + 10/60 ) }}}
{{{ d = 3*( t70/60+ 10/60 ) }}}
{{{ d = 3*(4/3) }}}
{{{ d = 4 }}} km
OK