<PRE><B>Question 1189223</B>
let x equal the total disance.


3/4 * x + 1/9 * x + 10 = x


multiply 3/4 * x by 9/9 and multiply 1/9 * x by 4/4 and multiply 1 * x by 36/36 to get:


27/34 * x + 4/36 * x + 10 = 36/36 * x


combine like terms to get:


31/36 * x + 10 = 36/36 * x


subtract 31/36 * x from both sides of the equation to get:


10 = 36/36 * x - 31/36 * x


combine like terms to get:


10 = 5/36 * x


multiply both sides of the equation by 36/5 to get:


36/5 * 10 = 36/5 * 5/36 * x


simplify to get:


72 = x


the duck flies 3/4 of the way = 3/4 * 72 = 54
the duck walks 1/9 of the way = 1/9 * 72 = 8
the duck swims 5/36 of the way = 10


the total distance traveled by the duck is 54 + 8 + 10 = 72 kilometers.
this confirms the solution is correct.
the solution is that the duck traveled a total of 72 kilometers.


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