Two diggers

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

Correct answer:

r =  3:2

Step-by-step explanation:

r = t2:t1  3t2/t1 + 3t1/t2 = 13/18 t1t2 + t2t1 =  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=2ab±D=22.17±0.69 r1,2=1.083333±0.416667 r1=1.5 r2=0.666666667  r=r1=1.5=23=121=3:2

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