We are told that the group traveled an average of 12 miles per day. So, for example, after 1 day of travel, the traveled distance would be 12. After day two, they would have traveled 12 extra miles. That is
[tex]12+12=24\text{ = 2}\cdot12[/tex]So note that to calculate the traveled distance, we take the number of days and multiply it by the average rate of miles per day (12 miles per day). Let x be the total amount of days the group took to travel 2000 miles. So , according to what we just described, we have the equation
[tex]x\cdot12=2000[/tex]so, by dividing both sides by 12 we get
[tex]x=\frac{2000}{12}=\frac{1000}{6}=\frac{500}{3}=166.666[/tex]so, the group took about 167 to travel the entire trail.
