The Table shows some common scales used in a model railroading.For each scale,find the length of a model of an 82-foot long boxcar.Give the length of each model in inches. Scale Name/Scale N 1:160, S 1:64, O 1:48

1/160=x/82 solve for x

1/160=x/82

1•82=82
82/160=.5125

To find the length of the model of an 82-foot long boxcar in inches for each scale, you will need to multiply the length by the scale ratio.

1. For Scale N (1:160):
- Multiply 82 by the scale ratio of 1/160.
- 82 * (1/160) = 0.5125 feet
- To convert from feet to inches, multiply by 12.
- 0.5125 * 12 = 6.15 inches

Therefore, the model of an 82-foot long boxcar in Scale N would be approximately 6.15 inches long.

2. For Scale S (1:64):
- Multiply 82 by the scale ratio of 1/64.
- 82 * (1/64) = 1.28125 feet
- To convert from feet to inches, multiply by 12.
- 1.28125 * 12 = 15.375 inches

Therefore, the model of an 82-foot long boxcar in Scale S would be approximately 15.375 inches long.

3. For Scale O (1:48):
- Multiply 82 by the scale ratio of 1/48.
- 82 * (1/48) = 1.7083333 feet
- To convert from feet to inches, multiply by 12.
- 1.7083333 * 12 = 20.5 inches

Therefore, the model of an 82-foot long boxcar in Scale O would be approximately 20.5 inches long.

To find the length of the model boxcar in inches for each scale, we need to use the scale ratio given for each scale. The scale ratio represents the proportion of the model size to the real size.

Let's start with the N scale, 1:160. In this scale, one unit on the model represents 160 units in real life. To find the length of the model boxcar, we divide the real length of 82 feet by the scale ratio:

Length in inches = (82 feet / 12 inches per foot) / 160

Length in inches (N scale) = 82 / (12 * 160) = 0.035 inches

Therefore, the length of the model boxcar in the N scale would be approximately 0.035 inches.

Moving on to the S scale, 1:64. Similarly, in this scale, one unit on the model represents 64 units in real life. Using the same formula, we find:

Length in inches = (82 feet / 12 inches per foot) / 64

Length in inches (S scale) = 82 / (12 * 64) = 0.107 inches

Therefore, the length of the model boxcar in the S scale would be approximately 0.107 inches.

Lastly, let's calculate the length of the model boxcar in the O scale, 1:48:

Length in inches = (82 feet / 12 inches per foot) / 48

Length in inches (O scale) = 82 / (12 * 48) = 0.143 inches

Therefore, the length of the model boxcar in the O scale would be approximately 0.143 inches.

To summarize:
- In the N scale, the length of the model boxcar would be approximately 0.035 inches.
- In the S scale, the length of the model boxcar would be approximately 0.107 inches.
- In the O scale, the length of the model boxcar would be approximately 0.143 inches.