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Emily sees a ship traveling at a constant speed along a straight section of a river. She walks parallel to the riverbank at a uniform rate faster than the ship. She counts $210$ equal steps walking from the back of the ship to the front. Walking in the opposite direction, she counts $42$ steps of the same size from the front of the ship to the back. In terms of Emily\textquotesingle s equal steps, what is the length of the ship? (2021 Fall AMC 10A Problems, Question \#11) 
Overseas Competition->Knowledge Point->Calculation Modules
Let $x$ be the length of the ship. Then, in the time that Emily walks $210$ steps, the ship moves $210-x$ steps. Also, in the time that Emily walks $42$ steps, the ship moves $x-42$ steps. Since the ship and Emily both travel at some constant rate, $\frac{210}{210-x}=\frac{42}{x-42}$. Dividing both sides by $42$ and cross multiplying, we get $5(x-42)=210-x$, so $6 x=420$, and $x=70$. 