### Instruction: It takes four painters working at the same rate $1.25$ work-days to finish a job. If only three painters are available, how many work-days will it take them to finish the job, working at the same rate? Express your answer as a mixed number.### Response: To solve this problem, I need to find the rate of each painter and then use that to find the time for three painters.
Since four painters take $1.25$ work-days, that means one painter would take four times as long, or $5$ work-days.
This is the rate of one painter: $1$ job per $5$ work-days, or $\frac{1}{5}$ jobs per work-day.
Now, if three painters are working at this rate, they will do $\frac{3}{5}$ jobs per work-day.
To find how many work-days they need to finish one job, I need to divide $1$ by $\frac{3}{5}$.
This is the same as multiplying by the reciprocal, so I get $1 \div \frac{3}{5} = 1 \times \frac{5}{3} = \frac{5}{3}$.