"Not that I'm lazy, but before I enter upon an expedition, I'd like to know how much huffin' and puffin' is involved!" |

"What you need to know, Lou, is the gradient! Gradient tells you how steep your route is! Gradient can be expressed numerically in many ways. One common way to describe the average steepness or gradient between two points is to state the difference in elevation (ED) divided by the horizontal distance (HD): Take a look at this example: - The vertical distance (here, the difference in elevation between points 'A' and 'B') = 10,000 feet
- The horizontal distance from 'A' to 'B' = 5 miles
- Gradient = vertical distance (elevation difference (ED)) divided by horizontal distance (HD)
- The GRADIENT is 2000 feet per mile (10,000 feet divided by 5 miles)
Elevation difference may also be expressed in inches, meters or some other convenient unit; similarly, horizontal distance may be expressed in feet, kilometers, etc. Thus, the gradient may be stated as inches/foot, feet/mile, meters/kilometer, etc. |

The diagram on the right shows some slopes and their approximate gradients in feet/mile. |

"Let's look at an example close to home: the entrance to Boylan Hall at Brooklyn College. There are two ways to get up to the level of the doors from the quadrangle: - Using the steps.
- Using the ramp.
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"Well, of course the steps are steeper than the ramp! You go up the same amount but in a shorter distance! But I'd like to know how much steeper!!" |

"That's where gradient can help you! Let's take a closer look at what it's all about! Here's a photo of the steps:" |

"And here's a sketch of the steps!
If you look carefully, you'll see that to get from the ground to the level of the doors to the building (Platform 2), you have to go up nine 'risers', and across seven treads and Platform 1! Right?" |

"Now suppose, Lou, that I tell you the risers are 6 inches high, the treads are 12 inches across, and Platform 1 is 6 feet across! Now you tell me the following: " |

INSTRUCTIONS: Fill in each box and click the button to the right to see if your answer is correct.** ONLY USE NUMBERS, NOT LETTERS!**