Question

Two landscapers are filling containers with plants for a botanical garden. One landscaper has filled 3 containers and can fill 6 1/2 containers per hour. Another landscaper has filled 2 containers and can fill 7 containers each hour. After how many hours will the landscapers have filled the same number of containers?

Answer 1

To find the number of hours it will take for the landscapers to fill the same number of containers, we can set up and solve an equation using the information given.

Step-by-step explanation:

To find the number of hours it will take for the landscapers to fill the same number of containers, we need to set up an equation using the given information.

The first landscaper has filled 3 containers and can fill 6 1/2 containers per hour. So the equation for the number of containers filled by the first landscaper is 3 + (6 1/2)h, where h is the number of hours.

The second landscaper has filled 2 containers and can fill 7 containers per hour. So the equation for the number of containers filled by the second landscaper is 2 + 7h.

To find the number of hours when the landscapers have filled the same number of containers, we can set the two equations equal to each other and solve for h.

3 + (6 1/2)h = 2 + 7h

Subtracting 2 from both sides gives:

1 + (6 1/2)h = 7h

Subtracting (6 1/2)h from both sides gives:

1 = 7h - (6 1/2)h

Combining like terms gives:

1 = (7 - 6 1/2)h

1 = (13/2)h

Dividing both sides by 13/2 gives:

1 / (13/2) = h

Simplifying the division gives:

2/13 = h

So it will take approximately 2/13 of an hour, or about 9.2 minutes, for the landscapers to fill the same number of containers.