I’m sorry, that’s exactly the way the question is written! I was confused by it myself! I think it means:

Suppose you are at a concert and a singer’s voice is radio broadcast all around the world before reaching the radio you hold to your ear. This takes 1/8 seconds. If you’re close to the singer, you hear her voice in the air before you hear it from the radio. But, if you are far away, both signals will reach you at the same time. How many meters distant must you be for both signals to reach you at the same time??

My answer is either 1 meter or 8?? I think it's 8!

I'm still confused; however, my thinking is this.

Since it takes 1/8 second for the radio wave to hit your ear, the question may be asking "how far must your ear be from the singer for the sound wave to travel to your ear in 1/8 second?"
That is d = r*t
d = 343 m/s x 1/8 sec = about 43 meters.
Of course that all depends upon the speed of sound and that depends upon the humidity but this way of doing it at least makes a little sense to me. Check my thinking.

I would be interested in knowing if you think this is the correct approach.

I think you may be right, either way the question is to confusing to understand. It's giving to much information and then it doesn't really make sense to what they want to know. I think that's why I didn't get it! THANK YOU SO MUCH FOR ALL YOUR HELP DRBOB222!!

To solve this problem, let's break it down step by step:

First, we need to find the time it takes for the sound to travel from the singer to the listener through the air. Let's call this time "t1". According to the problem, this time is 1/8 seconds.

Next, we need to find the time it takes for the sound to travel from the singer to the listener through the radio. Let's call this time "t2". Since the problem states that both signals reach the listener at the same time when the listener is far away, we can assume that t2 is also 1/8 seconds.

Now, we can use the formula for the speed of sound to find the distance the sound travels during these times. The formula is: distance = speed × time.

The speed of sound in air is approximately 343 meters per second.

For the sound traveling through the air (t1), the distance is given by: distance1 = speed of sound × t1.

Similarly, for the sound traveling through the radio (t2), the distance is given by: distance2 = speed of sound × t2.

Since both distances are the same when the signals reach the listener at the same time, we can set them equal to each other and solve for the distance:

distance1 = distance2
speed of sound × t1 = speed of sound × t2

Now, let's substitute the known values:

343 × (1/8) = 343 × (1/8)

Simplifying the equation:

343/8 = 343/8

The distances cancel out, and we're left with:

1/8 = 1/8

So, indeed, both signals will reach the listener at the same time when they are 1 meter distant from the singer. Therefore, the correct answer is 1 meter, not 8 meters.