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Problem 573

AMC 12 late, AIME early

Geometry Difficulty 5.0 Find the answer

A bullet with a speed of $c=60 \frac{\mathrm{km}}{\text { hour }}$ was fired at a moving train, perpendicular to its direction. The bullet pierced a window pane on both sides of the train. How do these two holes lie relative to each other, if the bullet's speed was $c^{\prime}=40 \frac{\mathrm{m}}{\mathrm{sec}}$ and the width of the train was $a=4 \mathrm{~m}$ ?

Your answer

A number or a short expression. Spacing, $ signs and \frac vs / are all fine.

Official solution

The second arrow will be $a \frac{c}{c^{\prime}}=\frac{5}{3} \mathrm{~m}$ further back.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.