Question 1152113
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The solution from the other tutor is a perfectly good formal algebraic solution.<br>
If a formal algebraic solution is not required, here is an alternative method for solving the problem.<br>
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.<br>
So the ratio of the times required by the two hoses is 1:0.3, or 10:3.<br>
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.<br>
We know that working together the two hoses take 18 hours to fill the pool.<br>
So in 18 hours, Bob's hose fills 10/13 of the pool, and Jim's hose fills 3/13 of the pool.<br>
That means the number of hours required for Bob's hose to fill the whole pool by itself is {{{18*(13/10) = 23.4}}}; and the number of hours required for Jim's hose to fill the pool by itself is {{{18*(13/3) = 78}}}.<br>