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?

A 3 row table with 4 columns. The first column has blank, Marco, and Jaylyn. The second column has a question mark, StartFraction 1 Over 6 EndFraction, StartFraction 1 Over 5 EndFraction. The third column has, blank, t, t. The last column has blank, StartFraction 1 Over 6 EndFraction t, StartFraction 1 Over 5 EndFraction t.

Rate (part/hour)
Time (hours)
Part of Fence Painted
Distance (meters)

Answer 1

The heading that should be written above the first column of numbers in the table is 'Rate (part/hour)'. This column represents the part of the fence that Marco and Jaylyn can paint individually per hour. Adding their rates gives us their combined rate for painting the fence together.

Step-by-step explanation:

The student is trying to determine how long it would take for Marco and Jaylyn to paint a fence together given their individual times. The heading that should be written above the first column of numbers in the table should indicate the rate at which Marco and Jaylyn can work. Since the rate can be expressed as the part of work done per unit of time, the first column represents the Rate (part/hour).

Marco can paint 1/6th of the fence in one hour, and Jaylyn can paint 1/5th of the fence in one hour. To find out how quickly they would paint the fence together, we can add their individual rates. Therefore, when working together, Marco and Jaylyn's combined rate is 1/6 + 1/5 = 5/30 + 6/30 = 11/30 of the fence per hour.

Next, since 't' represents the time in hours it would take for them to paint the fence together, the third column indicates Time (hours), and the last column represents the Part of Fence Painted, which is the product of the rate and time.