if a certain amount of corn can feed 18 horses for 64 days how long will the same amount last 72 horses feeding at the same rate

Answer 1

To determine how long the same amount of corn will last for 72 horses when it can feed 18 horses for 64 days, we can use the concept of "horse-days."

First, calculate the total horse-days that can be supported by the corn:

\[ \text{Total horse-days} = \text{Number of horses} \times \text{Number of days} = 18 \text{ horses} \times 64 \text{ days} = 1152 \text{ horse-days} \]

Now, we'll find out how long this amount of corn will last for 72 horses. We'll set up the equation for horse-days using the number of horses and the number of days (\(d\)):

\[ 72 \text{ horses} \times d \text{ days} = 1152 \text{ horse-days} \]

Now solve for \(d\):

\[ d = \frac{1152 \text{ horse-days}}{72 \text{ horses}} = 16 \text{ days} \]

Thus, the same amount of corn will last for 72 horses for 16 days.