**Introduction**

In this lesson, you will perform unit conversions with speeds. When you do unit conversions for speeds, you may have units in the numerator and denominator that you need to change.

This video illustrates the lesson material below. Watching the video is optional.

**Unit Conversions for Speeds**

**Steps for Speed Unit Conversions:**

- Identify the units you know.
- Identify the units you want to get in the end.
- Determine what conversion factors you should use. You will need more than one.
- Arrange conversion factors so that unwanted units cancel out through cross-cancellation.

**Example 1**

The average horse can run about 25 miles per hour. (Remember per can mean divided by. Therefore, this can also be written as \(25 \space miles\div 1 \space hour\).) What is this speed in meters per second?

Start with what you know. The horse runs at 25 miles per hour, or \(\frac{25miles}{hour}\) , and you want to convert this to meters per second, or \(\frac{meters}{second}\). In other words, meters in the numerator and seconds in the denominator.

The first conversion factor to use is: \(1\space mile = 1609.34 \space meters\), This particular unit conversion is one that is easily looked up online; you don't necessarily have to have it memorized.

The expression can now be written as:

\begin{align*} &\frac{25 \;\color{red}\cancel{miles}}{1\; hour}\times\frac{1609.34 \;meters}{1 \;\color{red}\cancel{miles}} \end{align*}

Notice how the miles units cancel out. Now you need to change the hour into seconds. To do this, multiply by another conversion factor that can change hours into seconds: \(1\space hour = 3600\space seconds\).

\begin{align*} &\frac{25 \;\color{red}\cancel{miles}}{1\; \color{blue}\cancel{hour}}\times\frac{1609.34 \;meters}{1 \;\color{red}\cancel{miles}} \times \frac{1\;\color{blue}\cancel{hour}}{3600\;sec} \end{align*}

Now, hours can cancel each other out as well, and you are left with meters and seconds (meters in the numerator and seconds in the denominator), which is exactly what you wanted.

Now calculate to find the answer by using the zig-zag method:

\begin{align*} 25\div 1\times 1609.34\div 1\times 1\div 3600\end{align*}

This equals 11.175 meters per second, or since you want to round up, 11.18 meters per second.

Another method is to multiply the numerators across, then multiply the denominators across, and then simplify by dividing the numerator by the denominator to get the answer. Notice the answers using both methods are the same.

\begin{align*} \frac{25\times1609.34\times 1}{1\times 1\times 3600} = \frac{40233.5meters}{3600seconds} = \frac{11.18m}{1sec}\end{align*}

Therefore, if this horse is running at 25 miles per hour, it is also running at 11.18 meters per second.

**Things to Remember**

*Per*can also mean divided by.- Steps for speed unit conversions:
- Identify the units you know.
- Identify the units you want to get in the end.
- Determine what conversion factors you should use. You will need more than one.
- Arrange conversion factors so that unwanted units cancel out through cross-cancellation.

### Practice Problems

1. Alice was roller-skating down the street at a speed of 9 kilometers per hour (km/h). Use the fact that 1 kilometer is approximately equal to 0.6214 miles to convert this speed to miles per hour (mph). Round your answer to the nearest tenth.1 km = 0.6214 mi

Note that mph or miles per hour is the same as miles/hour or \(\dfrac{\text{miles}}{\text{hour}}\).

(

1 mi = 1.609 km

(

1 mi = 1609.344 m

1 h = 60 min

(

1 m = 3.2808 ft

1 min = 60 sec

(

1 m = 3.2808 ft

1 min = 60 sec

(

1 km = 1000 m

1 min = 60 sec

1 hour = 60 min

(

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