Question

Danny and his cousin Olivia are picking apples in their grandparents' orchard. Danny has filled 11 baskets with apples and is filling them at a rate of 5 baskets per hour. Olivia has 12 full baskets and will continue picking at 4 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 much fruit will they have picked by then? How long will that take?

Olivia and Danny have each filled ? baskets in ? hour(s)

Answer 1

Answer: Olivia and Danny have each filled 16 baskets in 1 hour

Explanation:

We can solve this using simultaneous equations.

Let h be the number of hours of picking apples when both have the same number of baskets

Danny already has 11 baskets. If he picks apples for 1 hour and fills them at the rate of 5 baskets per hour he will have filled a total of
11 + 5h baskets after h hours

Olivia has 12 baskets filled and is filling baskets at 4 baskets per hour

After h hours the number of filled baskets she has

= 12 + 4h

Equate the two

11 + 5h = 12 + 4h

Subtract 11 from both sides

11 - 11 + 5h = 12 - 11 + 4h

5h = 1 + 4h

Subtract 4h from both sides:

5h - 4h = 1

h = 1

Number of baskets filled after 1 hour (including the original baskets filled) = 11 + 5(1) = 16 = 12 + 4(1)

Answer: Olivia and Danny have each filled 16 baskets in 1 hour