解:设甲电线$x$米。
$x×({1-\frac {1} {3}} )+ ({2000-x} )×({1-\frac {1} {4}} )=1400$
$x×\frac {2} {3}+ ({2000-x} )×\frac {3} {4}=1400$
$\frac {2} {3}x+1500-\frac {3} {4}x=1400$
$\frac {3} {4}x-\frac {2} {3}x=1500-1400$
$\frac {1} {12}x=100$
$x=100\div \frac {1} {12}$
$x=1200$
$2000-1200=800 ({米} )$
答:甲电线$1200$米,乙电线$800$米$.$