If each of the x employees of a tech startup produces one unit of false hope every t minutes, how many units of false hope does the startup produce in a standard 17 hour workday?
This type of problem expects us to express a relationship between multiple variable by writing an equation that translates what our word problem tells us. This will likely be much easier if we simply choose values for each of our variables as we work through the problem.
We will start by choosing values for t. If each employee produces one unit of false hope every 30 minutes, we can calculate that each employee will produce 2 units each hour. If it takes merely 15 minutes instead, each employee will generate 4 units each hour instead. In other words, we see that dividing 60 minutes by the time it takes each employee to generate 1 unit, we get units per hour for one employee:
However, this is just for one employee for 1 hour. Say we have 10 employees. We must then multiply by 10 to calculate how much false hope all 10 employees will generate in 1 hour. But since we have x employees rather than 10, we would multiply by x instead:
Finally, we must figure out how much false hope all employees generate in not just 1 hour, but in our brief 17-hour work day. We must multiply our hourly output by 17 to get our final answer:
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