Math

QuestionSofia paraglides from a cliff 840 m high, landing 321 m away. When her travel ratio is 1:21: 2, find her distance from the cliff.

Studdy Solution

STEP 1

Assumptions1. Sofia starts paragliding from a cliff that is840 meters above the ground. . She lands a horizontal distance of321 meters away from the base of the cliff.
3. The ratio of the distance Sofia has traveled to the distance she has left to travel is 11.
4. We are asked to find her horizontal distance from the cliff when the above ratio is satisfied.

STEP 2

First, let's denote the total horizontal distance Sofia travels as $$. This distance is given as321 meters.

STEP 3

According to the problem, when the ratio of the distance Sofia has traveled to the distance she has left to travel is 1212, we need to find her horizontal distance from the cliff. Let's denote the distance she has traveled as dd and the distance she has left to travel as d - d.

STEP 4

We can write the ratio of the distance Sofia has traveled to the distance she has left to travel as d/(d)=1/2d/( - d) =1/2.

STEP 5

Now, we can solve this equation for dd. Multiply both sides by 2(Dd)2(D - d) to get rid of the denominator.
2d=Dd2d = D - d

STEP 6

olve the equation for dd by adding dd to both sides.
3d=D3d = D

STEP 7

Now, we can substitute the given value for $$ into the equation to find $d$.
3d=3213d =321

STEP 8

olve the equation for dd by dividing both sides by3.
d=321/3d =321 /3

STEP 9

Calculate the value of dd.
d=321/3=107metersd =321 /3 =107\, metersofia is107 meters away from the cliff when the ratio of the distance she has traveled to the distance she has left to travel is 22.

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