Question

The maximum speed recorded for a giant tortoise is \(0.11 \mathrm{~m} / \mathrm{sec}\). How many miles could a gaint tortoise travel in \(5.0 \mathrm{hr}\) ?

Short answer

1.23 miles

Step-by-step solution

- Convert speed to miles per hour

First, convert the speed from meters per second to miles per hour. We use the conversion factors: 1 mile = 1609.34 meters and 1 hour = 3600 seconds.The speed in miles per hour: \[0.11 \text{ m/s} \times \frac{1 \text{ mile}}{1609.34 \text{ m}} \times \frac{3600 \text{ s}}{1 \text{ hr}} = 0.246 \text{ miles/hr}\]

- Calculate distance traveled in 5 hours

Now, determine the distance the tortoise could travel in 5 hours by multiplying the speed in miles per hour by the time in hours.\[ \text{Distance} = 0.246 \text{ miles/hr} \times 5 \text{ hr} = 1.23 \text{ miles} \]

Key concepts

Speed Conversions

Understanding speed conversions is essential in various scientific fields, including chemistry. Here, we start with converting the speed of a giant tortoise from meters per second to miles per hour. It's crucial to use the appropriate conversion factors. One mile equals 1609.34 meters, and one hour equals 3600 seconds. To perform the conversion, remember the following steps:

• First, convert the speed from meters to miles by dividing by 1609.34.
• Next, convert from seconds to hours by multiplying by 3600.

So, for our example, the tortoise has a recorded speed of 0.11 meters per second. Using the conversion factors, the calculation is as follows:
\( 0.11 \text{ m/s} \times \frac{1 \text{ mile}}{1609.34 \text{ m}} \times \frac{3600 \text{ s}}{1 \text{ hr}} = 0.246 \text{ miles/hr} \). This gives us the speed in mile per hour which is 0.246 miles per hour.

Distance Calculation

Once we know the speed in the desired unit (miles per hour in this case), calculating the distance becomes straightforward. The basic formula is distance equals speed multiplied by time. Using our tortoise example:

• Speed of the tortoise: 0.246 miles per hour.
• Time traveled: 5 hours.

Applying the formula: \( \text{Distance} = 0.246 \text{ miles/hr} \times 5 \text{ hr} = 1.23 \text{ miles} \). Thus, in 5 hours, the giant tortoise can travel 1.23 miles. Always ensure your speed and time units match when performing these calculations.

Time Conversion

Time conversion is a critical step in many scientific problems. Often, you need to convert time from one unit to another to match the units in the rest of your calculation. In this problem, we had to divide and multiply correctly between seconds and hours. Here are key time conversion reminders:

• 1 hour = 3600 seconds
• 1 minute = 60 seconds
• To convert from seconds to hours, divide by 3600.
• To convert from hours to seconds, multiply by 3600.

For our exercise, converting speed involves understanding that \( \text{1 hour} = 3600 \text{ seconds} \). This is crucial for the correct conversion from meters per second to miles per hour. Such conversions are often required to standardize units in scientific calculations.