The number of hours walked varies inversely with the speed of the walker. if it takes sam 12 hours to complete his walking goal at 5 miles per hour, how long would it take him at 3 miles per hour?

We let k be the proportionality constant for the relationship between number of hours, h and speed of the walker, s. 

                        h = k/s
Substituting the known values,
                        12 = k/5
                          k = 60

For the second scenario,
                          h = k/s
Substituting the calculated value for k and the given value for speed,
                          h = (60)(3 miles/hour)
                         h = 20 hours
                         h = 20 hours

Therefore, it will take 20 hours to walk with a speed of 3 miles per hour.