Bill can do a job in 20 mins. Jim can do same job in 30 mins. How long would it take if they worked together? the solution that my author gives is: t/20 + t/30 = 1, with t being the time the job would take with both working together.

I, thinking the t was a 1--presbyopia rampans--set it up thus: 1/20 +1/30 = 1. I proceeded thus: 3/60 + 2/60 = 1 =5/60 (and here I veered sharply off the beaten path and instead of trying to make 5/60 = 1, I divided 60 by 5 and lo! I got 12 which happens to be the correct answer. I used this same approach with numerous other problems in this format and it always came out right. So...to solve this type of problem take the reciprocal of the time it takes for a to do the work, add it to the time it takes b, and then divide the denominator of the result by the numerator and Bob's your uncle!

Am I wrong here?

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