TITLE: Solving the equation $15=|135-60t|$ on $0\le{t}\le{5}$; two possible solutions
QUESTION [5 upvotes]: Ann is driving along a highway that passes through Boston. Her distance $d$, in miles, from Boston is given by the equation $d=\vert{135-60t}$| where $t$ is the time in hours since the start of her trip and $0\le{t}\le{5}$. Determine when Ann will be exactly 15 miles from Boston.
I have solved the equation $15=|135-60t|$ and I found two solutions by the mean of the absolute value by solving the equation $15=135-60t$ and after the calculation is found that $t=2$; or by solving the equation $-15=135-60t$ and after solving the equation is found that $t=2.5$. I am not clear in understanding the meaning of this exercise. What does the sign minus in the second equation express? When is Ann exactly 15 miles from Boston? I have only found that $t=2$ hours or $t=2.5$ hours. 
Would you help me please? Thank you in advance.

REPLY [2 votes]: There are two times when she is 15 miles away from Boston.  there are two values that have the same absolute value on the real number line x and -x, d=|135-60t| gets converted into:
$$15=135-60t$$  and $$-15=-135+60t$$  solving the first we get $$-120=-60t\implies 2=t$$ and the second one gives $$-150=60t\implies 2=t$$ EDIT of course by simply plugging in values we would get the table:
$$\begin {array}{c|c}d & t\\\hline 135 & 0 \\75 & 1\\15 &2 \\45 & 3 \end{array}$$
okay I messed up at first the point is t doesn't need to have only one solution.