Question 954056
if point C heard the explosion 12 seconds after it occurred, and sound travels at 1/3 kilometer per second, then the explosion must have been 4 kilometers away from point C.


If both points A and B heard it as the same time, then the explosion must have been exactly halfway between points A and B.


That puts the explosion on the circumference of a circle around point C and the perpendicular bisector of the line between points A and B.


Both conditions will be satisfied at the intersection of the circle with the line.


the perpendicular bisector of the line between points A and B is the line y = 5.


the location of the circle around point C depends on the scale of the graph.


the solution will be the intersection between the perpendicular bisector of the line between point A and B, and the circle surrounding the point C.


If the scale on the graph is one unit per kilometer, there will be no intersection and your problem will not have a solution.


The circle around point C is 4 km away from point C.


At 1 km per unit, that means the circle is 4 units away from point C on the graph.


As such, it will not intersect with the line y = 5 because the highest it will go is the point (-8,4).


here's a graph of that occurrence.


<img src = "http://theo.x10hosting.com/2015/030901.jpg" alt = "$$$" </>


If the scale on the graph is 4/5 of a unit per kilometer, there will be one intersection and your problem will have exactly one solution.


The circle around point C is 4 km away from point C.


At 4/5 km per unit, that means the circle is 5 units away from point C.


As such, it will intersect with the line y = 5 at the point (-8,5).


At that point, point C heard it 12 seconds after it occurred and points A and B heard it at the same time.


here's a graph of that occurrence.


<img src = "http://theo.x10hosting.com/2015/030902.jpg" alt = "$$$" </>


If the scale on the graph is 1/2 of a unit per kilometer, there will be two intersections and your problem will have exactly two solutions.


The circle around point C is 4 km away from point C.


At 1/2 km per unit, that means the circle is 8 units away from point C.


As such, it will intersect with the line y = 5 at the points (-14.24,5) and (-1.76,5).


At those points, point C heard it 12 seconds after it occurred and points A and B heard it as the same time.


here's a graph of that occurrence.


<img src = "http://theo.x10hosting.com/2015/030903.jpg" alt = "$$$" </>


If the scale on the graph is 1/3 of a unit per kilometer, there will be two intersections and your problem will have exactly two solutions.


The circle around point C is 4 km away from point C.


At 1/3 km per unit, that means the circle is 12 units away from point C.


As such, it will intersect with the line y = 5 at the points (-18.91,5) and (2.91,5).


At those points, point C heard it 12 seconds after it occurred and points A and B heard it as the same time.


here's a graph of that occurrence.


<img src = "http://theo.x10hosting.com/2015/030904.jpg" alt = "$$$" </>


Bottom line is the graphical solution depends heavily on what the scale of the map is.


That information is missing.


If, in fact, you did not mean that point C heard it 12 seconds after the explosion, but you meant that point C heard it 12 seconds after points A and B heard it, then you have a different situation and a different solution.