# Find the number of wagons

Algebra Level 3

An engine has a top speed $$S$$ when no wagons are attached to it. The speed reduces when wagons are attached. The reduction (from $$S$$) is proportional to the square root of the total number of wagons attached.

We have an engine with $$W$$ wagons attached to it already, which can move at a particular speed. If 7 wagons are added to this, the speed reduces by 10 mph. If another 20 are added, the speed further reduces by 20 mph. Find the initial number of wagons $$W$$.

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