Question

or Ben and his cousin Mary are picking apples in their grandparents' orchard. Ben has filled 15 baskets with apples and is filling them at a rate of 2 baskets per hour. Mary has 5 full baskets and will continue picking at 3 baskets per hour. Once the cousins get to the point where they have filled the same number of baskets, they will carry them to the barn and then eat lunch. How long will that take?

Answer 1

It will take Ben and Mary 10 hours to fill the same number of apple baskets, at which point they will take the baskets to the barn and have lunch.

Step-by-step explanation:

To find out when Ben and his cousin Mary will have filled the same number of baskets with apples, we need to set up an equation that will allow us to compare their progress. Ben starts with 15 baskets and continues to fill at a rate of 2 baskets per hour, and Mary starts with 5 baskets and fills at a rate of 3 baskets per hour.

Let's represent the number of hours it takes until they have the same number of baskets with the variable x. For Ben, we can model the number of baskets as
15 + 2x, and for Mary, the model is 5 + 3x.

We set the two models equal to each other to find the point when Ben and Mary will have the same number of baskets:

• 15 + 2x = 5 + 3x

Subtract 2x from both sides:

• 15 = 5 + x

Subtract 5 from both sides:

• 10 = x

So, it will take 10 hours before Ben and Mary have the same number of baskets filled.

After this time, they will carry the baskets to the barn and then eat lunch.