Go west 77° 51' 47"" from 124° 37'23"" W longitude. What is your longitude?

Your longitude is: 157º30'50""E

Explanation:

Adittion of Longitudes:

If they are in the same direction, we just add the values. We have to be careful that there is no longitude higher than 180 degrees, so, if the result of the sum is higher than this, we must subtract 360 by our value, and change direction.

For example

101W + 80W = 181W

360 - 181W = 179E

In this problem, we go from

77° 51' 47""W from 124° 37'23"" W

Same direction, means we need to sum the values.

Always start adding from the seconds

Worth remembering that each degree has 60 minutes, and each minute has 60 seconds.

47 seconds + 23 seconds = 70 seconds = 1 minute and 10 seconds. So we know that we are at 10"". The minute will be added with the minutes

So

51 minutes + 37 minutes + 1 minute (from the seconds addition) = 89 minutes = 1 degree and 29 minutes. Now, we know that we are at 29' 10"". We just have to find the degrees

77 degrees + 124 degrees + 1 degree = 202º

We are at 202º 29' 10"" W. This longitude is higher than 180º, so we must subtract 360º by this value, and change the hemisphere.

So

360º - 202º 29' 10""

The subtraction also starts from the seconds. However, we need to take a minute so we can add. There are no minutes, then we take a degree. Now we have

359º59'60"" - 202º 29' 10"" = 157º30'50""E

Your longitude is: 157º30'50""E