A blue rope is three times as long as a red rope. A green rope is 5 times as long as the blue rope. If the total length lf the three ropes is 508.26 meters, what is the length of the blue rope?
To find the length of the blue rope, we'll first set up equations based on the given information.
Let's assume the length of the red rope is "x" meters.
According to the problem, the blue rope is three times as long as the red rope. So, the length of the blue rope can be represented as 3x.
Similarly, the green rope is five times as long as the blue rope. Therefore, the length of the green rope can be represented as 5 * (3x) = 15x.
The total length of all three ropes is given as 508.26 meters. So, we can set up the equation:
x + 3x + 15x = 508.26
Simplifying the equation, we have:
19x = 508.26
To find the value of x, we can divide both sides by 19:
x = 508.26 / 19
Now, we can substitute the value of x back into the equation for the blue rope:
Blue rope = 3x = 3 * (508.26 / 19)
Evaluating the expression gives us the length of the blue rope.
R = 1/3B
G = 5B
R + G + B = 508.26
Substitute 1/3B for R and 5B for G in the second equation and solve for B.