Convert 120 kilometers to miles per hour.
Understand the Problem
The question is asking for the conversion of a distance measurement in kilometers to a speed measurement in miles per hour. To do this, we will first need to know the equivalent of kilometers in miles and then express that distance over the time unit of hours.
Answer
The speed in miles per hour can be calculated using the formula: $$ speed_{mph} = \frac{d_{km} \times 0.621371 \times 3600}{t_{sec}} $$
Answer for screen readers
The final speed in miles per hour is given by the equation: $$ speed_{mph} = \frac{d_{km} \times 0.621371 \times 3600}{t_{sec}} $$
Steps to Solve
- Identify the conversion factor for kilometers to miles
We know that 1 kilometer is approximately equal to 0.621371 miles. This is our conversion factor.
- Convert kilometers to miles
Letâ€™s denote the distance in kilometers as $d_{km}$. To convert this distance to miles, we can use the conversion factor: $$ d_{miles} = d_{km} \times 0.621371 $$
- Convert the time to hours if necessary
If the time duration is given in seconds, we need to convert it to hours for the speed measurement. There are 3600 seconds in one hour. So if $t_{sec}$ is the time in seconds, we convert it to hours using: $$ t_{hours} = \frac{t_{sec}}{3600} $$
- Calculate the speed in miles per hour
Now we can calculate the speed in miles per hour (mph) using the converted distance and time: $$ speed_{mph} = \frac{d_{miles}}{t_{hours}} $$
- Combine the conversions into one equation (if applicable)
If we directly know the distance in kilometers and the time in seconds, we can combine our equations: $$ speed_{mph} = \frac{d_{km} \times 0.621371}{\frac{t_{sec}}{3600}} $$
- Simplifying the speed formula
This simplifies to: $$ speed_{mph} = \frac{d_{km} \times 0.621371 \times 3600}{t_{sec}} $$
The final speed in miles per hour is given by the equation: $$ speed_{mph} = \frac{d_{km} \times 0.621371 \times 3600}{t_{sec}} $$
More Information
When converting between kilometers and miles or other units, itâ€™s essential to remember the specific ratios. Here, 1 kilometer is about 0.621371 miles, which allows us to easily find speeds in different units.
Tips
- Confusing the conversion factor: Make sure to use the correct value for kilometers to miles.
- Not converting time properly: If time is in seconds, it must be converted to hours by dividing by 3600.
- Mixing up the units in the final speed calculation.