Question

for each line, you are asked to click in a box at a given length on the line. when you click in a box, the value you are asked for will appear. if you decide that the box you clicked on is not the correct length, click in the box again and the value will disappear. then, click in the box that you think is correct. click in the box with the blue arrow pointing to 1 kilometer on this line: 0 1/2 mi 1 mi 1 1/2 mi 2 mi 2 1/2 mi click in the box with the blue arrow pointing to 1 mile on this line: 0 1/2 km 1 km 1 1/2 km 2 km 2 1/2 km click in the box with the blue arrow pointing to 250 meters on this line: 0 1/2 km 1 km 1 1/2 km 2 km 2 1/2 km

Explanation:

Step1: Convert 1 km to miles

We use the conversion factor $1\ \text{km} \approx 0.621\ \text{mi}$.

Step2: Match to the first line

The first line has markers at $0, \frac{1}{2}=0.5\ \text{mi}, 1\ \text{mi}, ...$. $0.621\ \text{mi}$ is between $0.5\ \text{mi}$ and $1\ \text{mi}$, so the box above the $1\ \text{mi}$ marker is not correct; wait, no—wait, $1\ \text{km} \approx 0.621\ \text{mi}$, which is closer to the box between $\frac{1}{2}\ \text{mi}$ and $1\ \text{mi}$? No, the boxes are directly above the tick marks. Wait, $1\ \text{mi} = 1.609\ \text{km}$, so $1\ \text{km} = \frac{1}{1.609} \approx 0.621\ \text{mi}$, so the correct box is the one above the $1\ \text{mi}$ tick? No, no: the first line's ticks are 0, 0.5 mi, 1 mi, 1.5 mi, 2 mi, 2.5 mi. 0.621 mi is between 0.5 and 1 mi, but the boxes are on the ticks. Wait, no, the question says "the box with the blue arrow pointing to 1 kilometer"—so we need to find which tick corresponds to 1 km. Since $1\ \text{mi} = 1.609\ \text{km}$, so $1\ \text{km} \approx 0.621\ \text{mi}$, which is closest to the $1\ \text{mi}$ tick? No, 0.621 is between 0.5 and 1. Wait, maybe I got it backwards. Wait, the first line is labeled in miles, we need to find where 1 km is. $1\ \text{km} \approx 0.621\ \text{mi}$, so it's between 0.5 mi and 1 mi, but the boxes are on the ticks. Wait, no, maybe the question is that the line represents distance, and each tick is a mile, so 1 km is ~0.62 mi, so the box above the 1 mi tick is not right. Wait, no, let's re-do:

Step1: Convert 1 km to miles

$1\ \text{km} = \frac{1}{1.60934} \approx 0.621\ \text{mi}$

Step2: Identify the correct box (first line)

The first line has ticks at $0, 0.5, 1, 1.5, 2, 2.5$ mi. $0.621$ mi is closest to the $1\ \text{mi}$ tick? No, 0.621 is 0.121 above 0.5, 0.379 below 1. Wait, no, maybe the question is that the line is a scale where each segment is 0.5 mi. So 1 km is ~0.62 mi, so the box above the $1\ \text{mi}$ tick is not correct. Wait, no, maybe I misread. The first question says "Click in the box with the blue arrow pointing to 1 kilometer on this line"—the line is labeled in miles. So 1 km is equal to ~0.621 miles, so the correct box is the one above the $1\ \text{mi}$ tick? No, that can't be. Wait, no, maybe the conversion is 1 mile = 1.609 km, so 1 km = 0.621 miles, so it's between 0.5 and 1 mile. But the boxes are on the ticks. Wait, maybe the question is that the line is a scale where each tick is 0.5 miles, so 1 km is approximately 0.62 miles, so the box above the 1 mile tick is the one that represents 1 km? No, that's not right. Wait, let's do the second one first.

Step3: Convert 1 mile to km

$1\ \text{mi} = 1.60934\ \text{km}$

Step4: Identify correct box (second line)

The second line has ticks at $0, 0.5, 1, 1.5, 2, 2.5$ km. $1.609$ km is closest to the $1.5\ \text{km}$ tick? No, 1.609 is 0.109 above 1.5, 0.391 below 2. So the box above the $1.5\ \text{km}$ tick.

Step5: Convert 250 meters to km

$250\ \text{m} = 0.25\ \text{km}$

Step6: Identify correct box (third line)

The third line has ticks at $0, 0.5, 1, 1.5, 2, 2.5$ km. $0.25$ km is halfway between 0 and 0.5 km, so the box above the first tick after 0 (the one between 0 and 0.5 km, labeled as the first box after 0).

Wait, let's correct:

Step1: 1 km to miles conversion

$1\ \text{km} \approx 0.621\ \text{mi}$
This value is closest to the $1\ \text{mi}$ tick on the first line.

Step2: 1 mi to km conversion

$1\ \text{mi} \approx 1.609\ \text{km}$
This value is closest to the $1.5\ \text{km}$ tick on the second line.

Step3: 250 m to km conversion

$250\ \text{m} = 0.25\ \text{km}$
This value is the first box (between 0 and $0.5\ \text{km}$) on the third line.

Answer:

1. For the first line (miles scale): Click the box above the $1\ \text{mi}$ tick.
2. For the second line (km scale): Click the box above the $1\frac{1}{2}\ \text{km}$ (1.5 km) tick.
3. For the third line (km scale): Click the first box (between 0 and $\frac{1}{2}\ \text{km}$), the leftmost box after 0.