Graphics Interpretation - Other Chart Types
The diagram shows a map of eight towns and the roads between them. The distances on the map are shown in centimeters and those distances have a scale of 3 centimeters to 40 miles. While the distances shown are to scale, other distances between towns cannot necessarily be found by measurement.
There is a radio station in Town E that is able to broadcast to a 100-mile radius from town.
From each drop-down menu, select the option that creates the most accurate statement based on the information provided.
A car that can travel 20 miles per gallon of gasoline uses approximately [[dropdown1]] gallons of gasoline to travel from Town C to Town D.
The radio signal from the station in Town E is guaranteed to reach [[dropdown2]] of the other seven towns.
Correct!
Since 20 miles is half of 40 miles, the car can travel half of 3 centimeters, or 1.5 centimeters, per gallon. So to find the amount of gasoline used, divide the distance in centimeters by 1.5.
The shortest distance from Town C to Town D is 8 centimeters, so the car uses
>$$8\div1.5\approx5.3$$gallons to make the trip. So 5 gallons is the best answer.
Incorrect.
The distance on the map is 8 centimeters, but the car does not travel 1 centimeter per gallon. Consider how many centimeters on the map the car can travel per gallon.
Incorrect.
Consider how many centimeters on the map the car can travel per gallon. You may have gotten this answer if you multiplied the number of centimeters by this conversion factor instead of dividing.
Incorrect.
[[snippet]]While the four towns that are adjacent to Town E will all be reached by the radio signal, they are not the only ones.
Great!
On the map, 100 miles corresponds to
>$$\displaystyle 100~ \mbox{miles} \cdot \frac{3~\mbox{cm}}{40~\mbox{miles}} = 7.5 ~\mbox{cm}$$,so any town that is less than 7.5 centimeters from Town E will be reached by the radio signal.
While you don't know direct distances, you can use the road distances to give a maximum distance, since the direct distance between two points is the shortest distance. If the shortest path between two towns is 7 centimeters or less, the direct distance is at most 7 centimeters. If the shortest path between two towns is 8 centimeters, it is possible that the direct distance is as much as 8 centimeters as well.
So Towns A, B, D, F, and H are all within 7.5 centimeters, or 100 miles, of Town E. Towns G and C could be as much as 8 centimeters away, meaning that they are not guaranteed to be reached by the radio signal. Thus, the correct answer is "five" towns.
Incorrect.
[[snippet]]If the shortest path between two towns is 8 centimeters, it is possible that the direct distance is as much as 8 centimeters as well.
Incorrect.
[[snippet]]Not all of the towns must be within 7.5 centimeters of Town E. While the distances shown are to scale, other distances between towns cannot necessarily be found by measurement.
