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You have a car that has a tank that can store $1$ unit of fuel. You need to get to a destination $1.5$ units of distance away. The car travels $1$ unit of distance on $1$ unit of fuel. You can deposit fuel along the route, but capacity is never more than $1$ unit. What is the minimum amount of fuel you need to make the trip?
My attempts at a solution: a solution would have the car having $1$ unit of fuel at $0.5$ metres equal. So it is not making any unnecessary returns. So the problem can be reduced to the minimum amount of fuel required to transport $1$ unit of fuel a distance of $0.5$.
I know it should be about $2-2.9$ units. Here is a drawing of using $2.9$ units:
Is there a way to optimize this?
Edit: I cannot see how this is the same as the camel problem, because the camel problem would give an answer of $3$, when $2.9$ is possible.