a dog runs back and forth between its two owners, who are walking toward one another. the dog starts running when the owners are 10 m apart. if the dog runs with a speed of 3 m/s and the owners each walk with a speed of 1.3 m/s how far has the dog traveled when the owners meet

when I did this problem, I divided half of the total distance (10 m) by 1.3 m/s because I thought that if the owners were going to meet each other they would each travel 5 m. the way this problem is worked out, though, the owners' speeds are combined and then divided by the total distance. I got the right answer, but I was wondering if anyone knew if my way could also be correct or if I just got lucky. Thanks-

How long does it take for the owners to meet? time= 10/(2*1.3) seconds

What velocity did the dog travel during this time?

distancedog=velocitydog*timedogran

Your way of solving the problem is logical, but let me explain the correct approach that takes into account the combined velocity of the owners.

To find out how far the dog has traveled when the owners meet, we need to find the time it takes for the owners to meet first.

Let's assume the distance the dog has traveled when the owners meet is "d" meters.

The combined velocity of the owners is the sum of their individual velocities, which is 1.3 m/s + 1.3 m/s = 2.6 m/s.

To find the time it takes for the owners to meet, we can use the formula:

Time = Distance / Velocity

In this case, the total distance the owners need to cover to meet is 10 meters. So the time it takes for them to meet is:

Time = 10 m / 2.6 m/s ≈ 3.846 seconds

Now, since the dog starts running when the owners are 10 meters apart and its speed is 3 m/s, we can calculate the distance the dog has traveled:

Distance = Speed × Time

Distance = 3 m/s × 3.846 s = 11.538 meters

Therefore, the dog has traveled approximately 11.538 meters when the owners meet.

In conclusion, your way of dividing half of the total distance by 1.3 m/s is not the correct approach because it does not consider the combined velocity of the owners. The correct approach involves finding the time it takes for the owners to meet using their combined velocity, and then calculating the distance the dog has traveled based on its own speed and that time.