Given :
One truck travels average speed of 53 miles per hour north
The other travels 50 miles per hour south
We need to find how many hours will two trucks be 206 miles apart.
Let the number of hours = h
Let the north direction is (+) and the south direction is (-)
The distance = speed * time
So, the distance traveled after h hours for the truck of average speed of 53 miles per hour north = +53 * h
And the distance traveled after h hours for the other of average speed of 50 miles per hour south = -50 * h
The difference between them will be 206 miles
So,
[tex]+53h-(-50h)=206[/tex]Solve for h :
[tex]\begin{gathered} 53h+50h=206 \\ 103\cdot h=206 \\ \\ h=\frac{206}{103}=2 \end{gathered}[/tex]So, the answer is : 2 hours
