Can anybody explain why the formula 'AB/A+B' is used to solve this math problem? "If it takes Adam 5 hours to paint a house, and it takes Ben 3 hours to paint a house, then how long does it take them if they work together?" The answer is 1 hour 52 minutes 30 seconds.

TabbyTom

In one hour Adam will paint 1/5 of the house and Ben will paint 1/3 of it. So an hour’s work for the two of them is (1/5 + 1/3) of the house, which is 3/15 plus 5/15, i.e. (A+B)/AB. The number of hours they will need to paint the whole house together is therefore the reciprocal of that number, which is AB/(A+B). Apr 01 05, 7:07 AM

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