Question

A woman and her dog are out for a morning run to the river, which is 2.0 km away. The woman runs at 2.5 m/s in a straight line. The dog is unleashed and bounds ahead at 4.5 m/s. The dog stops frequently to wait for her. For the final stretch of the run, the dog and the woman arrive at the river at the same time.

A) How long does it take the woman to reach the river?
B) How long does it take the dog to reach the river?

Answer 1

It takes the woman 800 seconds to reach the river at a speed of 2.5 m/s, while it takes the dog 16800 seconds to reach the river with 20 stops along the way.

Step-by-step explanation:

To calculate the time it takes for the woman to reach the river, we can use the formula: time = distance / speed. The distance to the river is given as 2.0 km, which is equal to 2000 m. The woman's speed is given as 2.5 m/s. Plugging in the values, we get: time = 2000 m / 2.5 m/s = 800 seconds.

To calculate the time it takes for the dog to reach the river, we need to determine how many times the dog stops and waits for the woman. We can divide the distance to the river by the distance the dog covers between each stop. The dog's speed is given as 4.5 m/s. Let's assume the dog stops every 100 m. The number of stops would be 2000 m / 100 m = 20 stops. The total stopping time would be 20 stops * 800 seconds per stop = 16000 seconds. Therefore, the total time for the dog to reach the river would be 800 seconds + 16000 seconds = 16800 seconds.