An engineer said be could finish a highway section in $3$ days with his present supply of a certain type of machine. However, with $3$ more of these machines the job could be done in $2$ days. If the machines all work at the same rate, how many days would it take to do the job with one machine?

Let m be the number of machines initially present. The total work in machine-days remains constant, giving the equation 3m equals 2 times (m plus 3). Solving this gives 3m equals 2m plus 6, so m equals 6. The total work requires 6 machines times 3 days, totaling 18 machine-days. Therefore, completing the job with one machine takes 18 days.

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