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# Lucy, Eduardo, Carmen, and Frank live on the same street. Eduardo's house is halfway between Lucy's house and Frank's house. Lucy's house is halfway between Carmen's house and Frank's house If the distance between Eduardo's house and Lucy's house is 150 ft, what is the distance in feet between Carmen's house and Eduardo's house?

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Represent the houses using the first letter of the people and as points on a segment. Since $E$ is halfway between $L$ and $F$, then $LE=EF$. Since $L$ is halfway between $C$ and $F$, then $CL=LF$. We also label $LE=150$ ft so that we need to find $CE$:

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