Word Problem (Circles/Rectangles) > > Question: The diagram shows a $400m$ running track. The "Bends" (semi cricles) are $100m$ and the "straights" are $100m$. Find the distance run by an athlete who runs $x$ metres out from the kerb. (Had to make the diagram in paint because the picture is not really clear so apologies) ![enter image description here]( * * * The part where I am stuck is what it means by runs $x$ metres out from the kerb. The answer is $400 + 2\pi x$ but not too sure how they got it

Your picture is misleading. The intent is ![enter image description here]( where the semicircles have length $100$ meters and the straights have length $100$ meters. Clearly running out from the kerb on the straights has no effect on the path length. Running out from the kerb by $x$on the circles increases the radius of the circle by $x$, so the circumference by $2 \pi x$.