Question

A plane requires 3300 gallons of fuel and 75 minutes to make a round trip to Prague, and it takes 5700 gallons of fuel and 130 minutes to make a round trip to Stockholm. A pilot is asked to use at least 94500 gallons of fuel and spend at least 2400 minutes to make round trips to Prague and Stockholm in his plane. Let P denote the number of round trips to Prague and S the number of round trips to Stockholm. 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.

Answer 1

Answer: The inequality that represents the condition based on the number of gallons of fuel will be:

`3300P +5700S \geq94500`

The inequality that represents the condition based on the number of minutes will be:

`75P +130S\geq2400`

Explanation:

Let P denote the number of round trips to Prague and S the number of round trips to Stockholm.

Since the plane requires 3300 gallons of fuel and 75 minutes to make a round trip to Prague and 5700 gallons of fuel and 130 minutes to make a round trip to Stockholm.

Then the inequality that represents the condition based on the number of gallons of fuel will be:

`3300P +5700S \geq94500`

The inequality that represents the condition based on the number of minutes will be:

`75P +130S\geq2400`

Answer 2

Fuel constraint:
.. 3300P +5700S ≥ 94500

Time constraint:
.. 75P +130S ≥ 2400