SOLUTION: A duck travels from point A to point B. If the duck flies 3/4 of the way, walks 1/9 of the way, and swims the remaining 10 kilometers of her trip, what is the total distance in kil

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Question 1189223: A duck travels from point A to point B. If the duck flies 3/4 of the way, walks 1/9 of the way, and swims the remaining 10 kilometers of her trip, what is the total distance in kilometers traveled by the duck?

Found 3 solutions by Theo, ikleyn, MathTherapy:
Answer by Theo(13342)   (Show Source):
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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.

Answer by ikleyn(52775)   (Show Source):
You can put this solution on YOUR website!
.
A duck travels from point A to point B.
If the duck flies 3/4 of the way, walks 1/9 of the way, and swims the remaining 10 kilometers
of her trip, what is the total distance in kilometers traveled by the duck?
~~~~~~~~~~~~~~~~~

The duck flies and walks, in total + = = = of the way. Hence, the duck swims = of the way. According to the problem, of the way is 10 kilometers; hence, of the way is 2 kilometers. It means that the entire way is 2*36 = 72 kilometers. ANSWER

Solved.

Answer by MathTherapy(10551)   (Show Source):
You can put this solution on YOUR website!

A duck travels from point A to point B. If the duck flies 3/4 of the way, walks 1/9 of the way, and swims the remaining 10 kilometers of her trip, what is the total distance in kilometers traveled by the duck?

Let distance from A to B, be D
Flying of the way, walking of the way, and swimming remaining 10 km results in:
27D + 4D + 360 = 36D ------ Multiplying by LCD, 36
31D + 360 = 36D
360 = 36D - 31D
360 = 5D
Distance from A to B, or