Calculating Distance: Solving a Velocity Problem with Runners A and B

[kfink85]

I just transferred to UMD and want to do well in this course because I need a C or better to get into my major (Psychology). So any help on the problem would be much appreciated. I got through most of them fine except this one. I am stumped.

1. Runner A is initially 4.0 mi west of a flagpole and is running with a constant velocity of 6.0 mi/h due east. Runner B is initially 3.0 mi east of the flagpole and is running wtih a constant velocity of 5.0 mi/h due west. How far are the runners from the flagpole when they meet?

Thanks in advance to anyone that can offer any explanations or answers.

 

[Tide]

HINT: How much time does it take for the runners to meet?

 

[quicknote]

I am happy to help you with this problem. To solve this velocity problem, we can use the formula distance = velocity x time. Let's break down the information given in the problem:

- Runner A is initially 4.0 mi west of the flagpole and is running with a constant velocity of 6.0 mi/h due east. This means that Runner A's velocity is 6.0 mi/h towards the east direction. We can also assume that Runner A has been running for a certain amount of time, which we will call t.
- Runner B is initially 3.0 mi east of the flagpole and is running with a constant velocity of 5.0 mi/h due west. This means that Runner B's velocity is 5.0 mi/h towards the west direction. Similarly, we can assume that Runner B has also been running for the same amount of time, t.

Now, we need to find the distance between the runners and the flagpole when they meet. This can be calculated by adding the distances traveled by Runner A and Runner B. Runner A has traveled a distance of 6.0 mi/h x t (since distance = velocity x time). Similarly, Runner B has traveled a distance of 5.0 mi/h x t. Therefore, the total distance between the runners and the flagpole when they meet is 6.0t + 5.0t = 11.0t.

To find the value of t, we can set up an equation using the information given in the problem. Since the runners are meeting, their total distance traveled must be equal. This can be represented as: 4.0 mi (initial distance of Runner A) + 6.0t (distance traveled by Runner A) = 3.0 mi (initial distance of Runner B) + 5.0t (distance traveled by Runner B). Solving for t, we get t = 0.5 hours.

Now, to find the distance between the runners and the flagpole when they meet, we can substitute the value of t into our earlier equation: 11.0t = 11.0 x 0.5 = 5.5 miles.

Therefore, the runners will be 5.5 miles from the flagpole when they meet. I hope this explanation helps you understand the problem better. Good luck with your course!