SOLUTION: working together, John and Mark can clean a fish tank in 30 minutes. If Mark works alone, he can clean it in 50 minutes. How long does it take John to clean the fish tank alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: working together, John and Mark can clean a fish tank in 30 minutes. If Mark works alone, he can clean it in 50 minutes. How long does it take John to clean the fish tank alone?      Log On


   

Question 998947: working together, John and Mark can clean a fish tank in 30 minutes. If Mark works alone, he can clean it in 50 minutes. How long does it take John to clean the fish tank alone?
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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Let  j  be the number of minutes for John to clean the tank.

Let  m  be the number of minutes for Mark to clean the tank.

Then John will clean  1%2Fj  part of the tank volume per minute.
Correspondingly,  Mark will clean  1%2Fm  part of the tank volume per minute.

Working together,  John and Mark will clean  1%2F30  part of the tank volume per minute.  It means that

1%2Fj + 1%2Fm = 1%2F30.       (1)

From the other part of the condition,  Mark is cleaning  1%2F50  part of the tank volume per minute working alone.  It means that

1%2Fm = 1%2F50.             (2)

Substitute  (2)  into  (1).  You will get

1%2Fj + 1%2F50 = 1%2F30.

Hence,

1%2Fj = 1%2F30 - 1%2F50 = %2850-30%29%2F1500 = 20%2F1500 = 2%2F150 = 1%2F75.

Thus  j = 75%2F1 = 75 minutes.

Answer.  It will take  75  minutes for Mark to clean the tank working alone.