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.

Final Answer:

r =  3:2

Step-by-step explanation:

r = t2​:t1​  3t2​​/t1​ + 3t1​​/t2​ = 13/18 t1​t2​​ + t2​t1​​ =  13/6  r + 1/r = 13/6 r2+1=13/6r  r2+1=13/6 r r2−2.167r+1=0  a=1;b=−2.167;c=1 D=b2−4ac=2.1672−4⋅1⋅1=0.6944444444 D>0  r1,2​=2a−b±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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algebrabasic operations and conceptsnumbersUnits of physical quantitiesthemes, topicsGrade of the word problem

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