You traveled three hours at a certain speed. If you had taken 1 minute less to do each mile you would have gone 30 miles farther than you actually did.
How far did you go?
Let the total time taken by the trveller to traverse one mile be p
minutes. Hence, in three hours the traveller would traverse 180/p miles.
If the trveller took (p-1) minutes to traverse one mile, then he
would traverse 180/(p-1) miles in three hours.
Accordingly, by conditions of the problem, we must have:
180/(p-1) - 180/p = 30
Or, 180/(p(p-1)) = 30
Or, p(p-1) = 6
Or, p^2-p-6 = 0
Or, (p+2)(p-3) = 0
Or, p=3, ignoring the negative value of p which is inadmissible.
Consequently, the required distance traversed by the traveller
in 3 hours is 180/3 = 60 miles.
Edited on April 29, 2008, 3:59 pm