Question

A 90–pound coil of cable is 300 feet long. If a 30–foot length is cut off, what is the weight in pounds of the remaining cable?​

Answer 1

Final Answer: When the $30 feet$ long portion is cut off from the $300 feet$ long cable coil weighing $90 pound$, the required weight in pounds, of the remaining $270 feet$ long cable is $81$.

Given:

There is a coil of cable of length $300 feet$. The weight of this whole length of cable coil is $90 pound$. A portion of the cable measuring the length of $30 foot$ is cut off from the full-length cable.

To Find:

Calculate the weight of the remaining length of the cable in pounds.

Explanation:

First, evaluate the length of the remaining portion of the cable.

In the second step, use the Unitary Method to solve this problem. In brief, the Unitary method is the mathematical approach to finding the per unit value from the available mathematical information and using this unit rate to arrive at the required calculation of the related parameters.

Step 1 of 3

The length of the remaining portion of the cable is

= the length of the intact cable - the length of the cut portion of the cable

$=300-30\\=270 feet$

Step 2 of 3

The weight of the $300 feet$ long intact cable (in pounds) $= 90$ .

Now, divide the weight by the length to get the weight per unit length.

So, the weight of the $1 foot$ long cable portion (in pounds) $=\frac{90}{300}\\ =\frac{3}{10}$.

Step 3 of 3

Multiply the weight per unit length by the remaining length of the cable.

Therefore, the weight of the $270 feet$ long cable portion (in pounds)

$=\frac{3}{10}*270\\=3*27\\=81$

Thus, the required weight of the remaining portion of the length $270 feet$ , which is obtained by cutting off a portion of $30 feet$ long from the original coil of cable length $300 feet$ , is $81 pound$.

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