Question

it would take marco 6 hours to paint a fence by himself. it would take jaylyn 5 hours to paint the same fence by herself. marco is creating this table to help him determine how long it would take them to paint the fence together. which heading should be written above the first column of numbers? marco: 1/6, t, (1/6)t; jaylyn: 1/5, t, (1/5)t. options: time (hours), distance (meters), rate (part/hour), part of fence painted

Explanation:

To determine the heading for the first column, we analyze the values. Marco's value is $\frac{1}{6}$ and Jaylyn's is $\frac{1}{5}$. In work - rate problems, the rate at which a person works is calculated as the reciprocal of the time taken to complete the job alone. Marco takes 6 hours to paint the fence, so his rate is $\frac{1}{6}$ part of the fence per hour, and Jaylyn takes 5 hours, so her rate is $\frac{1}{5}$ part of the fence per hour. The values $\frac{1}{6}$ and $\frac{1}{5}$ represent the rate (part of the fence painted per hour) at which Marco and Jaylyn work respectively. "Time (hours)" would be represented by the variable $t$ (the time they work together), "Distance (meters)" is not relevant here as we are dealing with painting a fence (a work - related problem, not a distance - related one), and "Part of Fence Painted" would be represented by $\frac{1}{6}t$ and $\frac{1}{5}t$ (the amount of the fence each paints in time $t$). So the heading for the first column should be "Rate (part/hour)".

Answer:

Rate (part/hour)