Algebra and Up:
Question: There is a hole in Paul's ceiling where rain drips in at a rate of 15 milliliters per minute. As Paul fixes the hole, the rain that gets through decreases linearly. It takes him 2 minutes and 36 seconds to complete the task. How much rain gets in as Paul fixes the hole?
(Hint: Graph the decreasing rate of dripping rain in terms of time. What shape is formed under the graph?)
Answer: 191/2 milliliters
Solution: When we graph the rate of dripping rain in terms of time, we get a line whose y-intercept is 15 milliliters per minute and whose x-intercept is 23/5 minutes. The shape formed under the graph is a triangle. To find how much rain gets in as Paul fixes the hole, we find the area of the triangle, which is 1/2 (15 milliliters per minute × 23/5 minutes) = 191/2 milliliters.
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