There is proportional relationship between your distance from a thunderstorm and the time from when you see lightning and hear thunder. If there are 9 seconds between lightning and thunder, the storm is about 3 kilometers away. If you double the amount of time between lightning and thunder, do you think the distance in kilometers also doubles? Justify your reasoning.

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d=kt

k(2*t)=2(k*t)=2*d
3(2*9)=2(3*9)=2*d
54=54=2*d

d/t=k
2*d/2*t=(2/2)(d/t)
2*d/2(9)
54/18
=3 kilometers or k

In order to determine whether doubling the time between lightning and thunder also doubles the distance in kilometers, we need to understand the nature of the proportional relationship between the two.

From the information provided, we know that there is a proportional relationship between the distance from a thunderstorm and the time between seeing lightning and hearing thunder. Specifically, a time of 9 seconds corresponds to a distance of approximately 3 kilometers.

To analyze whether doubling the time doubles the distance, we can consider the concept of proportionality. If the relationship is truly proportional, we would expect the ratio of distance to time to remain constant.

Let's calculate the ratio of distance to time based on the given values:
Ratio = Distance / Time
= 3 km / 9 s
= 1/3 km/s

Now, let's double the time:
New Time = 2 * 9 s
= 18 s

To maintain the proportional relationship, the new distance would need to be obtained using the same ratio as before:
New Distance = 1/3 km/s * 18 s
= 6 km

Based on this analysis, we can conclude that doubling the time between lightning and thunder would indeed double the distance in kilometers. The justification lies in the fact that the relationship between distance and time is proportional, which indicates that the ratio of distance to time remains constant.

To determine whether the distance in kilometers also doubles when the time between lightning and thunder is doubled, we need to examine the proportional relationship between the two.

Let's first establish the relationship between time and distance based on the given information. It is stated that if there are 9 seconds between lightning and thunder, the storm is about 3 kilometers away. From this, we can deduce that the ratio of time to distance is 9:3 or 3:1.

In other words, for every 3 seconds it takes for the sound of thunder to reach you after seeing lightning, the distance between you and the storm is 1 kilometer.

Now, if we double the amount of time between lightning and thunder, it becomes 2 times 9 seconds, which is 18 seconds. To determine if the distance doubles as well, we need to calculate the corresponding distance for this new time duration.

Using the established ratio, if 3 seconds correspond to a distance of 1 kilometer, then 18 seconds would correspond to (18/3) multiplied by 1 kilometer. Simplifying this, we find that 18 seconds corresponds to 6 kilometers.

Upon comparing the initial distance of 3 kilometers to the new distance of 6 kilometers, we can conclude that the distance in kilometers does indeed double when the time between lightning and thunder is doubled.

Therefore, the answer is that when you double the amount of time between lightning and thunder, the distance in kilometers also doubles.

since the relationship is proportional, the distance d and the time t are related by

d = kt

where k is a constant.

So, if you double the time, you have

k(2t) = 2(kt) = 2d

so, the distance also doubles.

Or, you can think of it like this.

d/t = k, a constant

If you now have 2t, you need 2d so that

2d/2t = (2/2)(d/t) is still k.