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posted by Katie .
Lisa can shovel her drive way in 35 minutes. Tom can shovel the same drive way in 40 minutes. How long will it take them to do the job together?

in one minute, Lisa can shovel 1/35 of the driveway
in one minute, Tom can shovel 1/40 of the driveway.
in one minute, they both can shovel 1/35 + 1/40 = 8/280 + 7/280 = 15/280 = 3/56 of the driveway.
So, it will take them 18 2/3 minutes working together.
If b is the time for both,
1/b = 1/35 + 1/40
b = 35*40/(35+40) = 18 2/3