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# Formulas for Problem Solving

## The d = rt formula

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Credit: Michael Kurras
Source: http://commons.wikimedia.org/wiki/File:Acela_old_saybrook_ct_summer2011.jpg

Have you ever ridden on a train? Have you heard of the high-speed Acela Express train? This train is becoming one of the fastest ways to travel on land, particularly if you live in the Northeastern United States.

#### News You Can Use

The Acela train travels at a top speed of 150 miles per hour and transports its riders between the cities of Boston, New York, Philadelphia, Baltimore, and Washington, D.C. While it does make stops in between, the high speed of the train has shortened travel and commute times. It is quickly becoming one of the fastest methods of ground travel.

Credit: SPUI
Source: http://commons.wikimedia.org/wiki/File:NEC_map.svg

According to railroad company Amtrak, the Acela train covers the 454 miles from Boston to Washington, D.C. in 6½ hours. Applying the formula for distance, distance=rate×time\begin{align*}\text{distance}=\text{rate} \times \text{time}\end{align*}, you can see that this means the train travels the route at an average speed of about 70 miles per hour. Amtrak has plans to speed up this rate in the future. It hopes to have the trip from Boston to Washington, D.C. shortened to 3 hours by the year 2040. Efficient train travel will be a way of the future!

#### Explore More

Take a virtual tour of the Acela train at the following link.

The trip from New York City to Boston takes around 3½ hours on the Acela train. Assuming that the train moves at an average speed of about 70 miles per hour, what is the distance that it travels?