Question

A civil engineer is making a scale model of a highway on ramp. The length is 4 inches. The actual length on the ramp is 500ft. Ik scale model is 1/125 but how many times as long as the actual on ramp is the model?

Answer 1

To find out how many times longer the actual on-ramp is than the model, we can use the following steps:

1. **Convert the model length to the same unit as the actual on-ramp:** Since the model's length is given in inches and the actual length is given in feet, we need to convert one of the measurements to the other unit so that they are comparable. Here, we will convert the model's length into feet. There are 12 inches in 1 foot, so to convert inches to feet, we divide by 12.

Model length in feet = Model length in inches / 12
Model length in feet = 4 inches / 12 inches per foot
Model length in feet = 1/3 foot

2. **Compare the actual length to the model length:** Once both lengths are in the same unit, we divide the actual on-ramp length by the model length to find out how many times longer the actual on-ramp is.

Times longer = Actual length / Model length
Times longer = 500 feet / (1/3 foot)

3. **Solve the division:** Now we solve the division by multiplying the actual length by the reciprocal of the model length.

Times longer = 500 feet * (3/1)
Times longer = 1500

So, the actual on-ramp is 1500 times longer than the model.

As for the mention of a scale of 1/125, this doesn't come into play in this specific comparison, as we are only comparing lengths. However, if we want to double-check the work, we can ensure that the scale is consistent with our findings.

Given a scale of 1/125, it means that 1 unit on the model represents 125 units in reality. If our model is 4 inches, that would mean:

Actual length at this scale = Model length * Scale factor
Actual length at this scale = 4 inches * 125
Actual length at this scale = 500 inches

Now, to convert this into feet:

Actual length at this scale in feet = 500 inches / 12 inches per foot
Actual length at this scale in feet = 41.6667 feet (approximately)

Now, this is not the actual length we've been given for the on-ramp (which is 500 feet), so it seems there might be some confusion with the scale provided. The scale factor is not needed when directly comparing the model's length to the actual on-ramp's length, as long as we convert into the same units for a fair comparison.

Answer 2

1500 Time the multiple of model scale is the actual length of the ramp.

Explanation:

Given:

Actual length of ramp is 500ft

Modelling scale is 1/125.

To Find:

how many times as long as the actual on ramp is the model.

Solution:

Actual length is 500 ft

When Civil engineer is modelling the ramp on model then it is about 1/125 of the actual length present at that site.

So

=500*1/125

=4 inches

So on model scale engineer took inches as a unit for scale.

Actual length is 500 ft and model length is 4 inches

So 1 ft corresponds to 12 inches hence 500*12=6000 inches

6000 inches corresponds to 4 inches on model scale

i.e it is about 1500 time multiple of the model scale.