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

Second well was
`103 (3)/(6)\ m` deep below the surface.

Explanation:

Given:

Depth of First well =
`46(2)/(3)\ m`

`46(2)/(3)\ m` can be Rewritten as
`(140)/(3)\ m`

Depth of First well =
`(140)/(3)\ m`

Also Given:

The second well had more water, and was
`77(5)/(6)\ m` deeper than the first well.

`77(5)/(6)\ m` can be Rewritten as
`(467)/(6)\ m`

Hence We can say that;

Depth of second well is equal to
`(467)/(6)\ m` plus Depth of First well.

framing in equation form we get;

Depth of second well =
`(467)/(6)+(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 =
`(467*1)/(6*1)+(77*2)/(3*2)= (467)/(6)+(154)/(6)`

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

Depth of second well =
`(467+154)/(6)=(621)/(6)\ m \ \ OR\ \ 103 (3)/(6)\ m`

Hence Second well was
`103 (3)/(6)\ m` deep below the surface.