Question

Two workers in a holiday boutique are filling stockings with small gifts and candy. Julia has already filled 10 stockings and will continue to fill them at a rate of 1 stocking per hour. Henry, who just arrived to help, can fill 2 stockings per hour. At some point, Henry will catch up with Julia and they will have completed the same number of stockings. How many stockings will each worker have filled by then? Write a system of equations, graph them, and type the solution.

Answer 1

Henry will catch up with Julia after 10 hours, and at that point, they will have both filled 20 stockings each.

Step-by-step explanation:

To find out when Henry will catch up with Julia in filling the stockings, we should set up a system of equations based on their rates of work. Let x be the number of hours it takes for Henry to catch up with Julia, and y be the total number of stockings filled by each by that time.

The system of equations that represents this situation would be:

• Julia's equation: y = 10 + x (Julia already filled 10 and fills 1 more per hour)
• Henry's equation: y = 2x (Henry fills 2 stockings per hour)

To solve the system, we equate the two equations and solve for x:

10 + x = 2x

x = 10 (hours)

Substitute x into either equation to find y:

y = 2 * 10 = 20

So, after 10 hours, they will both have filled 20 stockings each.