Question

Write a system of equations to describe the

situation below, solve using any method,
and fill in the blanks.
Jim and his cousin Jill are picking apples in
their grandparents' orchard. Jim has filled
10 baskets with apples and is filling them at
a rate of 2 baskets per hour. Jill has 8 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? How much fruit will they have
picked by then?
In
filled
hours, the cousins will each have
baskets with apples.

Answer 1

By setting up equations representing the number of baskets Jim and Jill have filled over time, we can calculate it will take 2 hours for them to have each filled the same number of baskets, which will be 14 baskets each.

Step-by-step explanation:

To solve for the time it will take for Jim and Jill to have picked the same number of baskets, we need to write a system of equations based on the information provided. Jim starts with 10 baskets and picks at a rate of 2 baskets per hour, and Jill starts with 8 baskets and picks at a rate of 3 baskets per hour.

Let t represent the time in hours, and b represent the number of baskets they have filled. The system of equations that models this situation is:

• Jim: b = 10 + 2t
• Jill: b = 8 + 3t

To find when they will have filled the same number of baskets, we set the equations equal to each other:

10 + 2t = 8 + 3t

Solving for t:

3t - 2t = 10 - 8

t = 2

So it will take 2 hours for Jim and Jill to have filled the same number of baskets. To find out how many baskets they will have each filled by then, we substitute t back into either equation:

b = 10 + 2(2)

b = 14

Thus, in 2 hours, the cousins will each have 14 baskets with apples.