John and Joan walk in opposite directions around a circular path, starting from the same point. The path has a radius of 50.0 meters. John walks at 1.00 m/s, Joan at 1.25 m/s. How long will it take for them to meet?

Can someone please explain this to me?! I keep getting it wrong and I only have one try left!

John: v1 = 1 m/s, distance “x”

Joan: v2=1.25 m/s, distance (2πR-x).
t= x/v1 =(2πR-x)/v2.
v2•x =(2πR-x) •v1 = 2πR•v1- v1•x,
x(v1+v2)= 2πR•v1,
x=2πR•v1/(v1+v2)=2•π•50•1/2.25=139.6 m.
t= x/v1=139.6/1 = 139.6 c.

To solve this problem, you need to find the time it takes for John and Joan to meet. Here are the steps to calculate that:

1. Determine the relative speed: Since John and Joan are walking in opposite directions, their speeds are combined. Add John's speed (1.00 m/s) and Joan's speed (1.25 m/s) to get the relative speed: 1.00 m/s + 1.25 m/s = 2.25 m/s.

2. Calculate the circumference of the circular path: The formula for the circumference of a circle is C = 2πr, where r is the radius. Given the radius of 50.0 meters, the circumference is C = 2π(50.0) = 100π meters (or approximately 314.16 meters).

3. Use the formula: Time = Distance / Speed. Since the distance John and Joan need to cover is equal to the circumference of the circular path (100π meters), and their relative speed is 2.25 m/s, the time it will take for them to meet can be calculated as: Time = (100π) / 2.25.

4. Calculate the result: Now you can plug in the values into the equation and evaluate it to find the time it takes for John and Joan to meet.

Time = (100π) / 2.25
≈ (100 * 3.1416) / 2.25
≈ 43.9829 seconds

Therefore, John and Joan will meet approximately after 43.9829 seconds.

Make sure to double-check your calculations and units to avoid any mistakes. Good luck with your final attempt!