Question

PASSAGE:
Julio and Sarah are on opposite sides of a river across from
each other. Sarah walks 20 feet down river and Julio walks 100
feet upriver. Julio stays on the riverbank and Sarah backs 9 feet
away from the river. They need to build a bridge for the shortest
path across the river.
Part 1: Find the length of the bridge.

Answer 1

The shortest distance separating Julio from Sarah is 111.8ft

To know the distance of the shortest bridge between Julio and Sarah, the following procedure must be carried out.

We know that Julio walked 100ft to one side and Sarah walked 20ft to the opposite side, that is, on the y-axis they are 120ft apart.

On the other hand, Julio stayed by the river and Sarah walked 9ft away from the river, that is, on the x-axis they are separated by a distance of 59ft (assuming that the width of the river is 50ft).

To know the linear distance that separates them, it is necessary to use the following formula of the Pythagorean theorem.

c² = a² + b²

c= $\sqrt{a^{2} + b^{2} }$

From this operation we know the value of a and b:

a = 120ft

b = 59ft

Now we just have to replace the values in the formula.

c = $\sqrt{120^{2} + 59^{2} }$

c = $\sqrt{14400 + 3481}$

c = $\sqrt{17881}$

c = 133,7

However, 133.5ft is not the value of the bridge distance because Sarah went 9ft away form the river. Then a portion must be subtracted from her to calculate the exact portion of the distance above the river.

For this we must calculate the distance that separates them that is above the Earth, for this we use the same mathematical formula.

c = $\sqrt{20^{2} + 9^{2} }$

c = $\sqrt{400 + 81}$

c = $\sqrt{481}$

c = 21,9ft

So the distance a part of the Earth covers is 21.9ft. To find out how far the bridge should be over the river, we subtract 21.9ft from the total distance 133.7ft

133,7ft - 21,9ft = 111,8ft

Note: This question is incomplete because it has missing information (the length and width of the river).

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