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.

The road between Towns G and H goes through the mountains. The speed limit on the mountain road is 30 miles per hour, while it is 60 miles per hour on all the other roads.

From each drop-down menu, select the option that creates the most accurate statement based on the information provided.

A person who travels at the speed limit takes approximately [[dropdown1]] when traveling from Town D to Town H by going through Town G than by going through Town E.

The shortest path from Town A to Town F is approximately [[dropdown2]] miles.

That's right! To find how the two times compare, you can compare the entire lengths of the two routes. This is convenient because the route through Town E is 9 centimeters, which is 120 miles (3×40). It takes exactly 2 hours to drive 120 miles at 60 miles per hour (the speed limit). The path from Town G to Town D is >$$\displaystyle5 \mbox{ cm}\cdot \frac{40 \mbox{ miles}}{3 \mbox{ cm}} = \frac{200}{3} \mbox{ miles}$$ long. At 60 miles per hour, it would take >$$\displaystyle\frac{200}{3} \mbox{ miles} \cdot \frac{1 \mbox{ hour}}{60 \mbox{ miles}} = \frac{200}{180} \mbox{ hours} = \frac{10}{9} \mbox{ hours}$$ to drive. The path from Town G to Town H is 40 miles long, and at 30 miles per hour, it would take >$$\displaystyle40 \mbox{ miles} \cdot \frac{1 \mbox{ hour}}{30 \mbox{ miles}} = \frac{4}{3} \mbox{ hours}$$ to drive. All together, it takes >$$\frac{10}{9}+\frac{4}{3} = \frac{22}{9} = 2\frac{4}{9}\mbox{ hours}$$ to drive from Town D to Town H through Town G. Since $$\frac{4}{9}$$ is approximately $$\frac{1}{2}$$, it takes approximately half an hour, or 30 minutes, longer than driving through Town E.

Incorrect.

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Recheck your math. You may need to multiply hours by 60 to convert your answer to minutes.

Incorrect.

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The differences in distance and speed limit do not exactly balance each other out, so this answer is incorrect.

Incorrect.

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You may have gotten this answer if you did not adjust the speed limit for the road from Town G to Town H since it goes through the mountains. The question states that the speed limit on this road is 30 miles per hour.

Incorrect.

While it might look like the straight line distance is approximately 9 centimeters, or 120 miles, there is no path that is that short.

Correct!

The shortest path from Town A to Town F is 11 centimeters long on the map, going through Towns D and E. To convert 11 centimeters to miles, multiply by $$\frac{40}{3}$$.

>$$\displaystyle11 \mbox{ cm}\cdot \frac{40 \mbox{ miles}}{3 \mbox{ cm}} = \frac{440}{3} \mbox{ miles}\approx 146.7\mbox{ miles}$$

So 145 miles is the best answer.

Incorrect.

While the path through Towns B and C is approximately this long, that is not the shortest path.

15 minutes less

the same amount of time

10 minutes longer

30 minutes longer

120 miles

145 miles

175 miles