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subtract equation 2' from equation 1' 24y - 24z = 2 dividing the whole equation by 2 12y - 12z = 1 ------equation 4 multiply equation 3 with 12 and equation 4 with 5 5y + 5z = 1 60y + 60z = 12 ----equation 3' 12y - 12z = 1 60y - 60z = 5 -----equation 4' add equation 4' and equation 3' 120y = 17 y = 17/120 substitute the value of y to equations 1 and 3 4x + 4y = 1 4x + 4(17/120) = 1 4x = 1 - 68/120 4x = 13/30 x = 13/120 5y + 5z = 1 5(17/120) + 5z = 1 5z = 1 - 85/120 5z = 7/24 z = 7/120 to get the time for each to finish the job alone, get the reciprocal of the rates. y = 17/120 t(y) = 120/17 days t(y) = 7.06 days x = 13/120 t(x) = 120/13 days t(x) = 9.23 days z = 7/120 t(z) = 120/7 days t(z) = 17.14 days

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