Two oil Wells are 4 km and 6 km from the river. The points along the river are 8 km apart. Find the common loading point on the river, using the shortest amount of pipe.
To find the common loading point on the river using the shortest amount of pipe, we need to first determine the distance between the two oil wells along the river.
We can start by drawing a diagram and labeling the given information:
River:
____________________
A B
Oil Wells:
A - 4 km
B - 6 km
Points along the river: 8 km apart
Now, let's calculate the distance between the two oil wells along the river:
Distance between A and B = Distance from A to common point + Distance from common point to B
Let's assume that the common loading point on the river is C.
Distance from A to C + Distance from C to B = 8 km
Since the two points along the river are 8 km apart, the distance from A to C + the distance from C to B must equal 8 km.
Let's represent the distances from A to C and from C to B as x and y, respectively:
x + y = 8
We also know that the distance between A and B is 10 km (4 km + 6 km).
Now, we can set up another equation based on the Pythagorean theorem:
x^2 + 8^2 = 10^2
Simplifying the equation, we get:
x^2 = 100 - 64
x^2 = 36
x = 6 km
Now, substitute the value of x into the first equation:
6 + y = 8
y = 2 km
Therefore, the distances from point C to A and B are 6 km and 2 km, respectively.
To find the common loading point on the river, we can measure 6 km from oil well A along the river and 2 km from oil well B along the river. The common loading point, point C, will be located there.
Using this method, we can find the common loading point on the river using the shortest amount of pipe.