Bob and james are finishing the roof of a house. working alone, bob can shingle the roof in 14 hours. james can shingle the same roof in 18 hours. how long will it take them working together to shingle the roof? round your answer to the nearest hundredth if necessary.
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we know that Bob can do the whole job in 14 hours, how much of the work has he done in 1 hour only?  well since he can do the whole lot in 14 hours in 1 hour he has only done 1/14 th of the job.

we know that James can do it in 18 hours, a bit slower, so in 1 hour he has done only 1/18 th of the job.

let's say it takes both of them working together say "t" hours, so in 1 hour Bob has done (1/14) of the work whilst James has done (1/18) of the work, the whole work being t/t or 1 whole, so for just one hour that'd 1/t done by both Bob and James.

answer: y=0 if that is what u r looking for

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: