# How far could the plane travel before it made its return?

A fighter plane had enough fuel to last a 6-hour flight. The speed of the wind and the speed of the plane made up a total of 1500km/h when the plane was flying in the direction of the wind during its mission. On its return trip, the total speed was reduced to 1200km/h as the plane was traveling against the wind. How far could the plane travel before it made its return?

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Suppose that the plane flies for $t$ hours on the outbound leg; clearly it travels $1500t$ km. On the inbound leg it will fly for $6-t$ hours, so it will cover $1200(6-t)$ km. Thus, we must choose $t$ so that
$$1500t=1200(6-t)\;.$$