It takes 5 minutes to fill an empty aquarium to a depth of 5/8 meters.

Question

What is the unit rate in minutes per meter?

Write your answer in simplest form.

Answer 1

To find the unit rate in minutes per meter, we first determine how many meters the aquarium is filled per the time it takes to fill it.

The aquarium is filled to a depth of $\frac{5}{8}$ meters in 5 minutes.

Now, we can calculate the unit rate by dividing the total time by the depth filled:

$$\text{Unit Rate}=\frac{\text{Time}}{\text{Depth}}=\frac{5\text{ minutes}}{\frac{5}{8}\text{ meters}}$$

To divide by a fraction, we multiply by its reciprocal:

$$\text{Unit Rate}=5\text{ minutes}\times \frac{8}{5}{\text{ meters}}^{-1}$$

The 5s in the numerator and denominator cancel out:

$$\text{Unit Rate}=8\text{ minutes per meter}$$

Thus, the unit rate of filling the aquarium is $\boxed{{\displaystyle 8}}$ minutes per meter.

Answer 2

the correct answer is js 8 ??

Answer 3

Yes, the unit rate calculated is indeed $8$ minutes per meter. This means that it takes $8$ minutes to fill $1$ meter of depth in the aquarium.

To summarize the calculation:

1. The aquarium is filled to a depth of $\frac{5}{8}$ meters in $5$ minutes.

2. To find the time it takes for $1$ meter, we use the formula:

   $$\text{Unit Rate}=\frac{\text{Time}}{\text{Depth}}=\frac{5\text{ minutes}}{\frac{5}{8}\text{ meters}}$$

   This simplifies to:

   $$5\times \frac{8}{5}=8\text{ minutes per meter}$$

So the answer is correctly given as $\boxed{{\displaystyle 8}}$ minutes per meter.

Answer 4

my answer need to be in simplest form.

Answer 5

Let's revisit the problem and clarify the expression of the answer to ensure it's in its simplest form.

We initially found that:

$$\text{Unit Rate}=\frac{5\text{ minutes}}{\frac{5}{8}\text{ meters}}=5\times \frac{8}{5}=8\text{ minutes per meter}.$$

The answer $8\text{ minutes per meter}$ is already in its simplest form, as it is a whole number.

If you want to express this in fraction form, it can be represented as:

$$\frac{8}{1}\text{ minutes per meter}.$$

Since $\frac{8}{1}$ is also $8$, there are no further simplifications needed.

Thus, whether as $8$ or $\frac{8}{1}$, both are considered the simplest forms.

If you're looking for a fractional representation that does not include whole numbers or if you want it in terms of the fraction of minutes per meter, the best answer remains:

$$8\text{ minutes per meter}.$$

Let me know if that addresses your request or if there’s anything more specific you're looking for!