Question 1155818
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The (corrected) solution by tutor @josgarithmetic is a typical good formal algebraic approach.<br>
If a formal algebraic solution is not required, you can solve the problem informally, using basically the same calculations, with just a few quick mental calculations.<br>
If I were to solve this problem by the quickest possible method, I would do it something like this.<br>
The first machine works for a total of 30 minutes; since it takes that machine 40 minutes to do the job alone, in those 30 minutes it does 3/4 of the job.<br>
That means the second machine, which works for 15 minutes, does 1/4 of the job.<br>
And that means it would take the second machine 60 minutes to do the whole job alone.<br>
Note if you finish the formal algebraic solution suggested by tutor @josgarithmetic, those are exactly the same calculations you do.