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Geometry

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The grade of a road or a railway road bed is the ratio rise/run, usually expressed as a percent. For example, a railway with a grade of 5% rises 5 ft for every 100 ft of horizontal distance.

1. The Johnstown, Pennsylvania, inclined railway was built as a "lifesaver" after the Johnstown flood of 1889. It has a 987-ft run at a 71% grade. How high does this railway lift its passengers?

2. The Fenelon Place Elevator railway in Dubuque, Iowa, lifts passengers 189 ft to the top of a bluff. It has an 83% grade. How long is this railway?

3. The Duquesne Incline Plane Company's roadway in Pittsburgh, Pennsylvania, climbs Mt. Washington, located above the mouth of the Monongahela River. It reaches a height of 400 ft with a 793-ft incline. What is its grade?

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