A woman and her dog are out for a morning run to the river, which is located 4.56 km away. The woman runs at 3.27 m/s in a straight line. The dog is unleashed and runs back and forth at 5.23 m/s between his owner and the river, until she reaches the river. What is the total distance run by the dog (in meters)?
To find the total distance run by the dog, we need to know how many times the dog travels between its owner and the river.
First, let's determine the time it takes for the woman to reach the river.
Using the formula distance = speed × time,
the distance is 4.56 km = 4.56 × 1000 = 4560 m
the woman's speed is 3.27 m/s.
Rearranging the formula to solve for time:
time = distance / speed,
time = 4560 m / 3.27 m/s,
time ≈ 1396.33 s.
Now, let's determine the time it takes for the dog to travel back and forth between his owner and the river.
The dog's speed is 5.23 m/s, and it travels from the owner to the river and back. Therefore, the total distance traveled by the dog in one round trip is:
2 × distance from owner to river,
2 × 4560 m,
= 9120 m.
To find the time it takes for one round trip, we can use the formula time = distance / speed.
time for one round trip = 9120 m / 5.23 m/s,
time for one round trip ≈ 1744.93 s.
Now, to find the number of round trips the dog makes, we divide the time taken by the woman to reach the river by the time for one round trip.
number of round trips = time taken by the woman to reach the river / time for one round trip,
number of round trips ≈ 1396.33 s / 1744.93 s,
number of round trips ≈ 0.8.
Since the number of round trips needs to be a whole number, we can approximate it to the nearest whole number. In this case, the number of round trips is 1.
Therefore, the dog makes one round trip between the owner and the river.
Finally, the total distance run by the dog is the distance covered in one round trip, which is 9120 m.