Problem of the Week - Algebra and Up - Dec. 27, 2020 to Jan. 2, 2021

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.