SOLUTION: Eric can clean the garden in 5 hours. After working alone for 2 hours, Leo joined him. Together they finished the job in one more hour. How long would it take Leo to clean the gard

Algebra ->  Radicals -> SOLUTION: Eric can clean the garden in 5 hours. After working alone for 2 hours, Leo joined him. Together they finished the job in one more hour. How long would it take Leo to clean the gard      Log On


   

Question 1194893: Eric can clean the garden in 5 hours. After working alone for 2 hours, Leo joined him. Together they finished the job in one more hour. How long would it take Leo to clean the garden alone.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, how long Leo does the one job if work alone


1%2F5%2B1%2Fx, combined rate for Eric and Leo together.

Rest of description gives %281%2F5%292%2B%281%2F5%2B1%2Fx%29%2A1=1.
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2%2F5%2B1%2F5%2B1%2Fx=1
3%2F5%2B1%2Fx=1
1%2Fx=2%2F5
x=5%2F2
highlight%28highlight%28x=2%261%2F2%29%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


You should know how to solve the problem using formal algebra, similar to what is shown in the other response you have received.

But solving a problem like this using logical reasoning and simple arithmetic is valuable brain exercise.

Eric works a total of 3 hours on the job; since he can do the whole job in 5 hours, he does 3/5 of the job.

That means Leo, in working 1 hour, does 2/5 of the job.

And that means the amount of time Leo would need to do the whole job alone is 5/2 hours.

A different thought process for reaching the final answer is to note that in the last hour working together they do 3/5 of the job, while Eric does 1/5 of the job. That means Leo does 2/5 of the job in that hour; so he works twice as fast as Eric. Then, since it takes Eric 5 hours to do the job alone, it would take Leo half as much time, which is 2.5 hours.