Question

A 30 m chain was found to be 6 cm too long after chaining a
distance of 3500 m. It was tested again at the end of the day's
work and found to be 9 cm too long after chaining a total distance of 6000 m.
If the chain was corrected before the commencement of the work, find the true
distance.
​

Answer 1

Answer:

2651.75m

Step-by-step explanation:

(1) Error before starting the day work = 20cm too short = -0.2m

Error after measuring a length of 1250m it is found 10cm long = 0.1 m

Average error= (−0.2+0.1)2=-0.05m

L1= 30 - 0.05 = 29.95m

Measured distance =1250m

Correct length = L1L× measured distance =29.9530×1250 = 1247.92m

Correct length = 1247.92m

(2) Error at the end of the day work the chain found to be 30cm too long = 0.3m

Average error=(−0.05+0.3)2 =-0.125m

L1= 30 + 0.125m= 30.125m

Measured distance =2648 – 1250 =1398m

Correct length = L1L× measured distance =30.12530×1398 = 1403.83m

Total true length = 1247.92+1403.83 =2651.75m

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