We studied and solved tons of problems like this in engineering school, but it looks like MBA's have a tougher time with it:
(HT Joe Carter)YOU MIGHT THINK that MBA students at MIT can easily deduce how much water is in a bathtub, based on the flow of water in and out. But you'd be wrong! Said bathtub is just one example of a "system" with "stocks" (e.g., water level) and "flows." Other examples are greenhouse gases in the atmosphere, customers in a store, or money in your bank account. Researchers at MIT, Carnegie Mellon University, and George Mason University found that most of their students had trouble understanding even supposedly straightforward systems with one stock, one inflow, and one outflow. The researchers conclude that the poor performance reflects a fundamental flaw in how we think about accumulation.
2 comments:
Wait a minute. The proper solution to this problem requires an understanding of two variable calculus, if I am not mistaken. That's not quite enough math for some disciplines, but much much more than is necessary for most.
Actually, if you're talking about constant flows (which I assume this is), you can solve this with some pretty basic algebra.
Here's an example:
Suppose you have a 100-gallon tub that has 40 gallons of water in it. At the bottom is a hole that drains 10 gallons per minute (output) and the faucet is running that puts in 30 gallons per minute (input). How long will it take for the tub to fill?
ANSWER:
100 = 40 + (30 - 10)*t
100 = 40 + 20*t
60 = 20*t
t = 3 minutes
If there are multiple constant inputs and outputs, you just sum them and apply the same algebra.
It can get a bit more complex with non-constant flows, but the idea is the same.
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