An airplane consumes fuel at a constant rate while flying through clear skies, and it consumes fuel at a rate of 64 gallons per minute while flying through rain clouds. Let C represent the number of minutes the plane can fly through clear skies and R represent the number of minutes the plane can fly through rain clouds without consuming all of its fuel. 56C+64R < 900056C+64R<9000 According to the inequality, at what rate does the airplane consume fuel while flying through clear skies, and how much fuel does it have before takeoff? The airplane consumes fuel at a rate of gallons per minute while flying through clear skies, and it has gallons of fuel before takeoff. Does the airplane have enough fuel to fly for 60 minutes through clear skies and 90 minutes through rain clouds?

Let C represent the number of minutes the plane can fly through clear skies and R represent the number of minutes the plane can fly through rain clouds.

We have been given that an airplane consumes fuel at a rate of 64 gallons per minute while flying through rain clouds, so the fuel consumed in flying for R minutes in rain clouds will be 64R.

We have been given an inequality [tex]56C+64R<9000[/tex] which represents the total fuel consumed in flying through C minutes in clear skies and R minutes in rain clouds.

Since 64R represents the fuel consumed in flying for R minutes in rain clouds, so 56C will represent the fuel consumed in flying for C minutes in clear skies.

As the airplane consumes fuel at a constant rate while flying through clear skies, therefore, the airplane consumes fuel at a rate of 56 gallons per minute.

We can see from our inequality that 9000 represents the total fuel consumed in flying through clear skies and rain clouds, therefore, the airplane has 9,000 gallons of fuel before take off.

To find if the airplane have enough fuel to fly for 60 minutes through clear skies and 90 minutes through rain clouds, we will substitute C=60 and R=90 in our given inequality.

[tex]56*60+64*90<9000[/tex]

[tex]3360+5760<9000[/tex]

[tex]9120>9000[/tex]

As the fuel consumed by plane in flying for 60 minutes through clear skies and 90 minutes through rain clouds is 9120 gallons and 9120 is greater than 9,000, therefore, the plane have not enough fuel to fly for 60 minutes through clear skies and 90 minutes through rain clouds.