document.write( "Question 1152113: Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know that it takes 18 h using both hoses. They also know that Bob's hose, used alone, takes 70% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone? \n" ); document.write( "

Algebra.Com's Answer #774052 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The solution from the other tutor is a perfectly good formal algebraic solution.

\n" ); document.write( "If a formal algebraic solution is not required, here is an alternative method for solving the problem.

\n" ); document.write( "To fill the whole pool alone, Bob's hose take 70% less time than Jim's. So if the time required by Jim's hose is x, the time required by Bob's hose is x minus 70% of x, which is 0.3x.

\n" ); document.write( "So the ratio of the times required by the two hoses is 1:0.3, or 10:3.

\n" ); document.write( "In working together, then, the fraction of the job that Bob's hose does is 10/13, and the fraction Jim's hose does is 3/13.

\n" ); document.write( "We know that working together the two hoses take 18 hours to fill the pool.

\n" ); document.write( "So in 18 hours, Bob's hose fills 10/13 of the pool, and Jim's hose fills 3/13 of the pool.

\n" ); document.write( "That means the number of hours required for Bob's hose to fill the whole pool by itself is $\"18%2A%2813%2F10%29+=+23.4\"$ ; and the number of hours required for Jim's hose to fill the pool by itself is $\"18%2A%2813%2F3%29+=+78\"$ .

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