SOLUTION: Solve for x Working together Ben and Frank was 1,000 dishes in 3 hours. Ben works twice as fast as Frank. How long does it take Frank to wash dishes alone?

Question 1112621: Solve for x
Working together Ben and Frank was 1,000 dishes in 3 hours. Ben works twice as fast as Frank. How long does it take Frank to wash dishes alone?
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
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Solve for x
Working together Ben and Frank wash 1,000 dishes in 3 hours. Ben works twice as fast as Frank.
How long does it take Frank to wash dishes alone?
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I just solved it (in semi-joking form) at this link

https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Rate-of-work-word-problems.faq.question.1112619.html

https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Rate-of-work-word-problems.faq.question.1112619.html

But if you want to get the solution in the serious algebraic form, here it is.

Let  x  be the Frank's rate, measured in dishes per hour.


Then the Ben rate is 2x dishes per hour.


The combined rate of work is  x + 2x = 3x  dishes per hour.


We are given  3x * 3 hours = 1000 dishes,  or   


9x = 1000 dishes


Now divide both sides of this equation by x. You will get

9 = .


It means that Frank will make all the job in 9 hours, working alone.

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