SOLUTION: installing a dishwasher. A plumber can install a dishwasher in 50 minutes. If the plumber brings his apprentice, the job takes 40 minutes. How long would it take the apprentice

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Question 149079: installing a dishwasher. A plumber can install a dishwasher in 50 minutes. If the plumber brings his apprentice, the job takes 40 minutes. How long would it take the apprentice working alone to install the dishwasher?
Found 3 solutions by ankor@dixie-net.com, solver91311, Electrified_Levi:
Answer by ankor@dixie-net.com(22740)   (Show Source):
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A plumber can install a dishwasher in 50 minutes. If the plumber brings his apprentice, the job takes 40 minutes. How long would it take the apprentice working alone.
:
Let a = time required if the apprentice works alone
:
Let the completed job = 1;
:
+ = 1
Multiply equation by 50a to get rid of the denominators, results:
40a + 50(40) = 50a(1)
:
40a + 2000 = 50a
:
2000 = 50a - 40a
:
2000 = 10a
a =
a = 200 min working alone
:
:
Check solution:
40/50 + 40/200 =
4/5 + 1/5 = 1

Answer by solver91311(24713)   (Show Source):
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If the plumber can do the installation in 50 minutes, then he can do of the installation in 1 minute. Likewise, working together, the plumber and his apprentice can do of the job in a minute. We need to find out how many minutes it takes the apprentice by himself and we'll call that , so the apprentice by himself can do of the job in one minute. So we can write:

LCD for 40 and 50 would be 200, so:

So it would take the apprentice 200 minutes or 3 hours and 20 minutes to do the installation by himself (presuming, of course, that the apprentice could do it by himself at all).

Answer by Electrified_Levi(103)   (Show Source):
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