Final Answer:
The dog runs 130m away from its master in 8.0s and then runs halfway back in one-third the time, which is 2.67s.
Step-by-step explanation:
Initially, the dog’s speed can be calculated using the formula speed = distance / time. The dog’s speed when running away from its master is 130m / 8.0s = 16.25 m/s. When the dog runs halfway back, it covers a distance of 65m (half of 130m). Using the speed calculated earlier, the time taken to cover this distance can be found using the formula time = distance / speed, which gives us 65m / 16.25 m/s = 4s.
However, since the dog runs halfway back in one-third the time, the actual time taken is 4s / 3 = 1.33s.
In summary, the dog runs 130m away from its master in 8.0s and then runs halfway back in one-third the time, which is approximately 2.67s.