Question

A geologist found two underground wells that contained large deposits of water. The first well was 46 2/3 meters below the surface. The second well had more water, and was 77 5/6 meters deeper than the first well. How deep below the surface was the second well?

Answer 1

Answer:

Second well was  $103 \frac{3}{6}\ m$ deep below the surface.

Step-by-step explanation:

Given:

Depth of First well = $46\frac{2}{3}\ m$

$46\frac{2}{3}\ m$ can be Rewritten as $\frac{140}{3}\ m$

Depth of First well = $\frac{140}{3}\ m$

Also Given:

The second well had more water, and was $77\frac{5}{6}\ m$  deeper than the first well.

$77\frac{5}{6}\ m$ can be Rewritten as $\frac{467}{6}\ m$

Hence We can say that;

Depth of second well is equal to  $\frac{467}{6}\ m$ plus Depth of First well.

framing in equation form we get;

Depth of second well = $\frac{467}{6}+\frac{77}{3}$

Now the denominators are common so we can solve the numerators

now to solve the fractions we need to make the denominator common we will use L.C.M we get;

Depth of second well = $\frac{467\times1}{6\times1}+\frac{77\times2}{3\times2}= \frac{467}{6}+\frac{154}{6}$

Now the denominators are common so we can solve the numerators.

Depth of second well = $\frac{467+154}{6}=\frac{621}{6}\ m \ \ OR\ \ 103 \frac{3}{6}\ m$

Hence Second well was $103 \frac{3}{6}\ m$ deep below the surface.