It takes Tim 4 minutes to build a snowman and his younger brother Jim 12 minutes to build a snowman. How long will it take them to build a snowman working together?

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This is an interesting problem.  What you are looking for is a length of time less than 4 minutes which will give Tim a fraction of his completed snowman and his younger brother another fraction of a completed snowman when added together produce a "whole" snowman.Don't panic.  Let's use 3 minutes.  If Tim can build an entire snowman in 4 minutes, then he can finish 3/4 of a snowman in 3 minutes. Now his younger brother needs 12 minutes to build his snowman and if he only worked at building a snowman for 3 minutes then he would complete 3/12 or 1/4th of a snowman.  Together Tim's 3/4th completed plus his brother's 1/4th completion rate of the snowman means in 3 minutes time they can both complete the snowman.