An airplane consumes fuel at a constant rate while flying through clear skies, and it consumes fuel at a rate of $x$ gallons per minute while flying through rain clouds. Let $y$ represent the number of minutes the plane can fly through clear skies and $z$ represent the number of minutes the plane can fly through rain clouds without consuming all of its fuel. 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?

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Q. An airplane consumes fuel at a constant rate while flying through clear skies, and it consumes fuel at a rate of

x

gallons per minute while flying through rain clouds. Let

y

represent the number of minutes the plane can fly through clear skies and

z

represent the number of minutes the plane can fly through rain clouds without consuming all of its fuel. 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?

Find Rate and Total Fuel: We need to find the rate of fuel consumption in clear skies and the total fuel before takeoff.
Define Variables: Let $r$ be the rate of fuel consumption in clear skies (gallons per minute).
Given Inequality: Let $t$ be the total fuel before takeoff (gallons).
Isolate Variables: Given the inequality: $r \cdot x + y \cdot z \leq t$
Assume Time Allocation: We need to isolate $r$ and $t$ from the inequality.
Rewrite Inequality: Assume $x$ is the number of minutes in clear skies and $y$ is the number of minutes in rain clouds.
Need More Information: Rewriting the inequality: $r \cdot x + y \cdot z \leq t$
Unable to Solve: To find $r$ , we need more information about $x$ , $y$ , and $z$ .
Unable to Solve: To find $r$ , we need more information about $x$ , $y$ , and $z$ .Without specific values for $x$ , $y$ , and $z$ , we can't solve for $r$ and $t$ .