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# Formulas for Problem Solving

## The d = rt formula

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MPH to KPH
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## Real World Applications – Algebra I

### Topic

Converting from MPH to KPH

### Student Exploration

There are major differences driving in the United States and driving in the United Kingdom (and possibly other countries, too!). For example, people drive on different sides of the road. In the US, people usually drive on the right side of the road. In the UK, people drive on the left side of the road.

Speed limit is also different. The units are different. In the US, speed limit signs are given in miles per hour. See below.

In the UK, these speed limit signs mean are talking about kilometers per hour. See below

Even though these two signs have the same number, they don’t represent the same thing. If you’re from the United States, would you want to go just as fast or slower than what the sign says? Which speed limit is higher?

We can find out by using a formula to convert the number of kilometers to miles. We know that 1 mile=1.609 kilometers\begin{align*}1\ mile = 1.609\ kilometers\end{align*}. With this information, we can multiply any number of miles by 1.609 to find its equivalence in kilometers.

For the example above, to find out how many kilometers is equal to 50 miles, we use the formula. Let k\begin{align*}k\end{align*} represent the number of kilometers, and m\begin{align*}m\end{align*} represent the number of miles we’re going to convert.

So, k=1.609m\begin{align*}k = 1.609 m\end{align*}

k=1.60950k=80.45 kilometers\begin{align*}& k = 1.609 ^* 50\\ & k = 80.45\ kilometers\end{align*}

So, if we saw the “50kph” sign in the UK, we probably don’t want to drive 50 miles per hour. We’d probably get a speeding ticket!

### Extension Investigation

See if you can figure out a formula to convert the number of kilometers to miles, given the information above. What is the conversion factor and why?

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