SOLUTION: Suppose the one worker can shovel snow from a sidewalk in 50 minutes and another worker can shovel it in 30 minutes. How long will it take if they work together?

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Question 505051: Suppose the one worker can shovel snow from a sidewalk in 50 minutes and another worker can shovel it in 30 minutes. How long will it take if they work together?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
These sorts of problems are based on multiple resources working together to complete 1 whole job.
So each resource contributes a fraction of the work.
.
One man who can do the whole job in 50 minutes.
So, he does 1/50 of the job per min.
.
Another man who can do the whole job in 30 minutes.
So, he does 1/30 of the job per min.
.
x = number of minutes to do the whole job working together
.
(1/50+1/30)*x = 1
.
((30+50)/1500)*x = 1
.
80x / 1500 = 1
.
80x = 1500
.
x = 75/4
.
x = 18 3/4 minutes
.
Done.