Question 936926
{{{ 15 }}} oxen eat ( 1 field ) / ( 80 days )
{{{ 1 }}} ox eats ( 1 field ) / ( 15*80 days )
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{{{ 20 }}} cows eat ( 1 field ) / ( 80 days )
{{{ 1 }}} cow eats ( 1 field ) / ( 20*80 days )
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Add their rates of eating to get their rate eating together
Let their rate eating together = ( 1 field ) / ( d days )
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{{{ 6*( 1/1200 ) + 2*( 1/1600 ) = 1/d }}}
Multiply both sides by {{{ 4800d }}}
{{{ 24d + 6d = 4800 }}}
{{{ 30d = 4800 }}}
{{{ d = 160 }}}
6 oxen and 2 cows eat 1 field of grass in 160 days
check:
{{{ 6*( 1/1200 ) + 2*( 1/1600 ) = 1/d }}}
{{{ 6*( 1/1200 ) + 2*( 1/1600 ) = 1/160 }}}
Multiply both sides by {{{ 40 }}}
{{{ 6/30 + 2/40 = 1/4 }}}
{{{ 1/5 + 1/20 = 5/20 }}}
{{{ 4/20 + 1/20 = 5/20 }}}
OK