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Question
Hi, although this might seem like a homework problem, it actually is not. It is from an online worksheet. Take a look at the following word problem about inverse proportions:

- 5 taps can fill a large container in 8 hours. If we use 10 taps, how long will it take to fill the container?

- My calculations:
  - 10*8=80
  - 80/5=16
  - Final answer: 16 hours
- My answer that I keep getting is 16 hours, however, whenever I check the answer page, it keeps saying that my answer is incorrect. Is it?

Answer
OK. Here's how I approached the problem. If 5 taps take 8 hours to fill some volume, then twice the number of taps (10) should be able to fill it in half the time (4 hours).

This problem boils down to figuring out how fast the container is filled for a given number of taps; in other words we are considering RATES of flow. More formally, we could have calculated

(8 hours)/(5 taps) = 1.6 hours/tap. Using this, we can calculate the time it takes to fill the container as a function of how many taps we have, that is

total hours = (hours/tap)(taps); note how the units work out (it's always good to check units when doing calculations). For this case, we have (1.6 hours/tap)(5 taps) = 4 hours.

Doing the unit checking thing, your calculations become

(10 taps)(8 hours) = 80 tap・hours, which is fine but not really relevant. Then you calculate

(80 tap・hours)/(5 taps) = 16 hours, which is in the correct units but not a solution for the right problem. The quantity (tap・hours) is really a volume since "tap" refers to a flow rate (e.g., liters/hour) and hours is time, so that, using the relation

(something/time)・time = something, we have (liters/hour)・(hours) = liters.

Your answer of 16 hours refers to how long 5 taps would take to fill 80 tap・hours, which again is not really relevant. We already know how long 5 taps takes to fill the volume in question (which is never specified, but doesn't need to be), i.e., 8.

Hope this helps. You may need to read it a few times! Keep up the effort.

Randy

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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