A penguin walks 10 feet in 6 seconds. At this speed: 1. How far does the penguin walk in 45 seconds? 2. How long does it take the penguin to walk 45 feet?

Steps to Solve

1. Calculate the speed of the penguin

First, we need to find the speed of the penguin by using the formula for speed, which is:

$$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $$

Given that the penguin walks 10 feet in 6 seconds, the speed is:

$$ \text{Speed} = \frac{10 \text{ feet}}{6 \text{ seconds}} = \frac{5}{3} \text{ feet/second} $$

2. Determine the distance walked in 45 seconds

Next, we use the speed we calculated to find out how far the penguin walks in 45 seconds using the same speed formula rearranged to find distance:

$$ \text{Distance} = \text{Speed} \times \text{Time} $$

Substituting the values we have:

$$ \text{Distance} = \left(\frac{5}{3} \text{ feet/second}\right) \times 45 \text{ seconds} $$

3. Calculate the distance

Now we calculate the distance:

$$ \text{Distance} = \frac{5 \times 45}{3} = \frac{225}{3} = 75 \text{ feet} $$

4. Calculate the time to walk 45 feet

We need to determine how long it takes the penguin to walk 45 feet. We can use the formula rearranged to find time:

$$ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $$

Substituting the known distance and speed:

$$ \text{Time} = \frac{45 \text{ feet}}{\frac{5}{3} \text{ feet/second}} $$

5. Calculate the time

Now we calculate the time:

$$ \text{Time} = 45 \times \frac{3}{5} = \frac{135}{5} = 27 \text{ seconds} $$