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

We can start solving this problem by using the rate of work formula:

Work = rate x time

We can use this formula to find the time it takes for Danny and Olivia to fill the same number of baskets.

Let's say that the number of baskets they will fill before lunch is "n".

We know that Danny is filling baskets at a rate of 5 baskets per hour and Olivia is filling baskets at a rate of 4 baskets per hour. So, we can write the following equation:

n = 5t + 11 (Danny's work)

n = 4t + 12 (Olivia's work)

We can set the two equations equal to each other and solve for t:

5t + 11 = 4t + 12

t = 1

So, it will take them 1 hour to fill the same number of baskets.

Now that we know the time it takes for them to fill the same number of baskets, we can use that information to find the number of baskets they will have filled by then.

We know that Danny is filling baskets at a rate of 5 per hour and has already filled 11 baskets, so we can use the work formula to find the number of baskets he will have filled by then:

Work = rate x

Hope this helps!