Help! With Surveying Problem

Here is the problem:

Two brass monuments set on a shady sidewalk have a known, verified horizontal separation of 99.96 ft. A surveyor measures between the monuments with a tape and reads 99.99 ft at a temperature of 83 degrees Fahrenheit, holding a tension of 15 lb while the tape is fully supported.

The length (ft) of the surveyor's tape between the 0 and 100 marks while the temperature remains at 83 degrees Fahrenheit is most nearly:

A 99.95

B 99.97

C 100.03

D The question cannot be answered with the information given

Here is the solution:

99.96 x

------ = -----

99.99 100

x=99.97 ft

The correct answer is B

Can someone tell me why this solution works?

I cant recall that exact formula for temperature correction, but it looks like they are using a simple ratio method with the known tape length and the adjusted length for the temperature.

I have never seen this method used before for this type of problem. They didn't use the temperature correction formula, only the ratio shown above. I was just wondering why the ratio solution works in this instance.

ARJ said:

I have never seen this method used before for this type of problem. They didn't use the temperature correction formula, only the ratio shown above. I was just wondering why the ratio solution works in this instance.

Click to expand...

The tape is supposed to be 100 ft, but we don't know yet.

The tape is divided to 100 sections ---> No matter what the tape is shorter/longer than 100 ft, we still have 100 sections on that tape.

The surveyor tensions the tape under high temperature, and measures between 02 monument. The result is 99.99 sections (because I don't know whether the tape is really 100 ft or not)

The key is "the tape is divided to 100 sections"

The correct distance between 02 monuments is 99.96 ft.

---> Correct length of the tape = 99.96 ft x 100 sect/99.99 sect = 99.9699 ft

Hope this help.

Makes sense. Thanks relieved. That does helps a lot.