Answer:
[tex]Total = 72\ km[/tex]
Step-by-step explanation:
Given
[tex]Fly = \frac{3}{4}[/tex]
[tex]Walk = \frac{1}{9}[/tex]
[tex]Swim = 10km[/tex]
Required
Determine the total distance travelled
First, we need to calculate the fraction of the distance where the duck swim, using the following equation:
[tex]Swim + Fly + Walk = 1[/tex]
[tex]Swim + \frac{3}{4} + \frac{1}{9}= 1[/tex]
Collect Like Terms
[tex]Swim = 1 - \frac{3}{4} - \frac{1}{9}[/tex]
Take L.C.M
[tex]Swim = \frac{36 - 27 - 4}{36}[/tex]
[tex]Swim = \frac{5}{36}[/tex]
This means that the duck swim 5/36 of the journey.
So, we have:
[tex]\frac{5}{36} * Total = 10km[/tex]
Multiply through by [tex]\frac{36}{5}[/tex]
[tex]\frac{36}{5}* \frac{5}{36} * Total = 10km * \frac{36}{5}[/tex]
[tex]Total = 10km * \frac{36}{5}[/tex]
[tex]Total = \frac{360km}{5}[/tex]
[tex]Total = 72\ km[/tex]
Hence, the duck travelled 72km
