Differential leveling is carried out from BM21 to BM22 along the three different routes but with same precision. The route lengths and respective difference in elevation as determined in the field work is indicated below.

Route

Length (km.)

Difference in elevation (m.)

1

8

16.010

2

9

16.100

3

10

16.160

Determine the correction, in millimeters, to the difference in elevation along route 1.

Determine the correction, in millimeters, to the difference in elevation along route 2.

Determine the correction, in millimeters, to the difference in elevation along route 3.

What is the adjusted difference in elevation between BM21 and BM22, in meters?

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1st: Compute for the weight for each route

\[
W = \frac{1}{L}
\]
\[
W_1 = \frac{1}{8}
\]
\[
W_2 = \frac{1}{9}
\]
\[
W_3 = \frac{1}{10}
\]
2nd: Compute for the summation of W

\[
\sum W = W_1 + W_2 + W_3
\]
\[
\sum W = \frac{1}{8} + \frac{1}{9} + \frac{1}{10}
\]
\[
\sum W = \frac{121}{360}
\]
3rd: Multiply W with the difference in elevation

\[
X = W \times DE
\]
\[
X_1 = \frac{1}{8} \times 16.010
\]
\[
X_1 = \frac{1601}{800}
\]
\[
X_2 = \frac{1}{9} \times 16.100
\]
\[
X_2 = \frac{161}{90}
\]
\[
X_3 = \frac{1}{10} \times 16.160
\]
\[
X_3 = \frac{202}{125}
\]
4th: Compute for the summation of X