# The time a fighter jet can stay in air is inversely proportional to the 4th power of its average speed. A jet loaded with 2000 liters of fuel can fly for 80 minutes at 600 km/h. What is the maximum...

The time a fighter jet can stay in air is inversely proportional to the 4th power of its average speed. A jet loaded with 2000 liters of fuel can fly for 80 minutes at 600 km/h. What is the maximum distance that the jet can cover.

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The time a fighter jet can stay in air is inversely proportional to the 4th power of its average speed. A jet loaded with 2000 liters of fuel can fly for 80 minutes at 600 km/h.

In 80 minutes, the distance traveled by the jet at 600 km/h is 600*(80/60) = 800.

If the average speed of the jet is increased to (1+x) the present value, where x is a positive fraction, its speed is now 600*(1 +x). But this decreases the time the jet can stay in the air by a factor (1+x)^4 which makes it 80/(1+x)^4 minutes. As a result, the distance the jet can fly is 600*(1 +x)*(80/60)*(1/(1+x)^4) = 800/(1+x)^3. However, if x is negative, 800/(1+x)^3 approaches infinity as 1 + x approaches 0.

Given the relation between the average speed of the jet plane and the time it can stay in air for, the jet could in fact cover any length of distance by reducing its average speed appropriately.