Two diggers

Two diggers should dig a ditch. If each of them worked just one-third of the time that the other digger needs, they'd dig up a 13/18 ditch together. Find the ratio of the performance of this two diggers.

Correct result:

r =  3:2

Solution:

r=t2:t1  t23/t1+t13/t2=13/18 t2t1+t1t2=13/6  r+1/r=13/6 r2+1=13/6r  r2+1=13/6 r r22.167r+1=0  a=1;b=2.167;c=1 D=b24ac=2.1672411=0.6944444444 D>0  r1,2=b±D2a=2.17±0.692 r1,2=1.08333333±0.416666666667 r1=1.5 r2=0.666666666667   Factored form of the equation:  (r1.5)(r0.666666666667)=0  r=r1=1.5=32=3:2

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