Write an inequality that represents the condition based on the number of gallons of fuel. Write an inequality that represents the condition based on the number of minutes.
Understand the Problem
The question asks to formulate inequalities based on the fuel and time conditions for a pilot making round trips to Prague and Stockholm. We need to create an inequality for gallons of fuel used and another for the total time spent based on the given values.
Answer
For gallons of fuel: $3300P + 5700S \geq 94500$; for minutes: $75P + 130S \geq 2400$.
Answer for screen readers
The inequalities representing the conditions are:
- For gallons of fuel:
$$ 3300P + 5700S \geq 94500 $$
- For minutes:
$$ 75P + 130S \geq 2400 $$
Steps to Solve
- Establishing the fuel inequality
To find the total fuel used for trips to both destinations, we can express it as:
The fuel used for trips to Prague is $3300P$, and for Stockholm, it is $5700S$.
Thus, the inequality based on the gallons of fuel is:
$$ 3300P + 5700S \geq 94500 $$
- Establishing the time inequality
Next, we calculate the total time spent on the trips. The time for Prague is $75P$, and for Stockholm, it is $130S$.
The inequality for the time spent is:
$$ 75P + 130S \geq 2400 $$
The inequalities representing the conditions are:
- For gallons of fuel:
$$ 3300P + 5700S \geq 94500 $$
- For minutes:
$$ 75P + 130S \geq 2400 $$
More Information
These inequalities can help the pilot plan how many trips to make to meet the fuel and time constraints. They can be solved graphically or using linear programming to find possible combinations of trips to Prague and Stockholm.
Tips
- Misunderstanding the coefficients: Ensure that the coefficients of $P$ and $S$ correspond correctly to the fuel and time required for each trip.
- Forgetting the inequality direction: The inequalities must reflect the "at least" conditions indicated in the problem.
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