The diagram below shows a city map of two towns, $A$ and $B$ separated by a river. A bridge is to be

Question

The diagram below shows a city map of two towns, $A$ and $B$ separated by a river. A bridge is to be built between the two towns, which are on opposite sides of a straight river of uniform width $r$km, and the two towns are $p$ km apart measured along the riverbank. Town $A$ is $1$km from the riverbank, and Town $B$ is $b$km away from riverbank. A bridge is to be built perpendicular to the riverbank at a distance of $x$km from Town $B$, measured along the riverbank, allowing traffic to flow between the two towns. Find the distance $x$, in terms of $b$ and $p$, such that the distance of travel between Town $A$ and Town $B$ can be minimised if $b>1$. (It is not necessary to verify that the distance is minimum.)

Accepted Answer

$x=\frac{b}{1+b}p$

2020 NYJC CT2 P2 Q3

2020 NYJC CT2 P2 Q3

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