A woman and her dog are out for a morning run to the river, which is located 3.51 km away. The woman runs at 3.48 m/s in a straight line. The dog is unleashed and runs back and forth at 5.50 m/s between his owner and the river, until she reaches the river. What is the total distance run by the dog (in meters)?
The woman runs for a total of
T = 3510m/(3.48 m/s) = 1009 seconds
Since the dog runs continuously, all you have to do is multiply 5.50 m/s by 1009 s for the distance the dog runs back and forth.
I get 5.55 km
To find the total distance run by the dog, we need to examine the distance covered by the dog while the woman runs to the river.
The woman runs at a constant speed of 3.48 m/s, covering a distance of 3.51 km (or 3510 meters). To determine how long it takes for the woman to reach the river, we can use the formula:
Time = Distance / Speed
Time = 3510 meters / 3.48 m/s
Time ≈ 1008.62 seconds
Since the dog runs back and forth between its owner and the river until she reaches the river, we need to determine how many round trips the dog makes. To do this, we can divide the total time taken by the woman to reach the river by the time taken for the dog to complete one round trip.
Time for one round trip = (Distance to river + Distance back to owner) / Speed
Time for one round trip = (3510 meters + 3510 meters) / 5.50 m/s
Time for one round trip ≈ 1276.36 seconds
Number of round trips = Total time taken / Time for one round trip
Number of round trips ≈ 1008.62 seconds / 1276.36 seconds
Number of round trips ≈ 0.79
Since the dog makes round trips, we have to consider the distance covered in both directions during each round trip. The distance covered by the dog during one round trip is:
Distance covered in one round trip = Distance to river + Distance back to owner
Distance covered in one round trip = 3510 meters + 3510 meters
Distance covered in one round trip = 7020 meters
To find the total distance run by the dog, we multiply the distance covered in one round trip by the number of round trips:
Total distance run by the dog = Distance covered in one round trip × Number of round trips
Total distance run by the dog ≈ 7020 meters × 0.79
Total distance run by the dog ≈ 5545.8 meters
Therefore, the total distance run by the dog is approximately 5545.8 meters.