Question

a duck travels from point A to point B. if the duckj 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

Answer 1

`Total = 72\ km`

Explanation:

Given

`Fly = (3)/(4)`

`Walk = (1)/(9)`

`Swim = 10km`

Required

Determine the total distance travelled

First, we need to calculate the fraction of the distance where the duck swim, using the following equation:

`Swim + Fly + Walk = 1`

`Swim + (3)/(4) + (1)/(9)= 1`

Collect Like Terms

`Swim = 1 - (3)/(4) - (1)/(9)`

Take L.C.M

`Swim = (36 - 27 - 4)/(36)`

`Swim = (5)/(36)`

This means that the duck swim 5/36 of the journey.

So, we have:

`(5)/(36) * Total = 10km`

Multiply through by
`(36)/(5)`

`(36)/(5)* (5)/(36) * Total = 10km * (36)/(5)`

`Total = 10km * (36)/(5)`

`Total = (360km)/(5)`

`Total = 72\ km`

Hence, the duck travelled 72km