This is a sample question:
A man jogs at a speed of 1.2 m/s. His dog waits 2 s and then takes off running at a speed of 4.1 m/s to catch the man. How far will they each have traveled when the dog catches up with the man?
The answer is 3.3931 m.
I just need to know the process to solve this practice problem so I can use that to solve my actual problem. I don't want to post my actual problem because I feel that could be akin to cheating if someone answered it.
Thank you in advance!
I felt like I should set the two equations equal to one another (since at a certain time their distances will be equal) but I'm failing to come up with a workable equation or process.
If you let t be the time in seconds the man started jogging.
then (t-2) is the duration the dog ran.
The distance travelled by both are the same, so calculate the distance travelled by the man and the dog. Equate them and solve for t.
Substitute t back into each of the distance expressions to make sure they are equal.
To solve this problem, you can start by setting up the equations for the distances traveled by the man and the dog.
Let's assume that the time taken by both the man and the dog is t when the dog catches up with the man.
The distance traveled by the man can be calculated using the equation:
Distance_man = Speed_man * Time = 1.2 m/s * t
The distance traveled by the dog can be calculated using the equation:
Distance_dog = Speed_dog * Time = 4.1 m/s * (t-2s)
Since the distances traveled by both the man and the dog are equal when they meet, we can set up an equation:
1.2 t = 4.1 (t - 2)
Solving this equation will determine the value of t, which represents the time when the dog catches up with the man.
1.2t = 4.1t - 8.2
-2.9t = -8.2
t = 2.8276 seconds (rounded to four decimal places)
Now, substitute the value of t back into either equation to find the distance traveled by both the man and the dog.
Distance_man = 1.2 m/s * 2.8276 s = 3.3931 m
Distance_dog = 4.1 m/s * (2.8276 s - 2 s) = 3.3931 m
Therefore, the man and the dog will have traveled 3.3931 meters each when the dog catches up with the man.
You can use this process to solve your actual problem by plugging in the appropriate values for the speeds and times in your specific question.