Problem
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Sliding ladder

A 10-foot ladder leans against a vertical wall. The base of the ladder slides away from the wall at a constant rate of 2 feet per second. How fast is the top of the ladder sliding down the wall at the instant the base is 6 feet from the wall?

Step 1 of 5
Step 1 of 5: Name the quantities

Step 1. Name the quantities

Give each changing quantity a letter, then record the rate you are given and the rate you are asked to find.

  1. \text{Let } x = \text{distance from the wall to the base (ft).}
  2. \text{Let } y = \text{height of the top on the wall (ft).}
  3. \text{Given } \frac{dx}{dt} = 2, \ \text{find } \frac{dy}{dt} \ \text{when } x = 6.

Related Rates Setup Builder: The Five-Step Method from CalcLearn, free AP Calculus study tools.