Natsu and Gray both run around a circular track. Theyboth started to run at the same time. Graystarted at the westernmost point of the track and runs counterclockwise, andGray takes about ninety-five seconds to run one lap of the track.Natsu runs clockwise and he passes Gray for the 1st time after eleven seconds.Natsu runs at 3 meters per sec (speed) and takes 80 seconds to run 1 lap of the track.

What are Natsu's coords when he passes Gray for the 1st time?

What I did:

I knew that it took Gray about 95 seconds to run1 full lap (which is equal to 2pi radians). So 2pi/95 rad/sec is his angular speed.

While Natsu's angular speed is then 2pi/80 rad/sec

Thereforespeed = angular speed * radius

I knew one of the speed was 3, so 3 = (2pi/80)*r, and solved for r to be 240/2pi = 120/pi

Then I knewθ = angular speed * time, so I found the θ to be 11 * 2pi/95

There I put everything into this:rcos(θ+pi), rsin(θ+pi)

Where I got the coords: (-28.52, -25.40) for when Natsu meets Gray for the first time.(So I got the answers correct here, the second question is where I need help).

What are Natsu's coords when he passes Gray for the second time?

This is the part I got lost on:

Ok, so I know Natsu's angular speed is 2pi/80

While Gray's angular speed is 2pi/95

What I tried doing was to find the time, throughθ = angular speed * time

So then θ = 2pi/80 * t (for Natsu)

And 2pi - θ = 2pi/95 * t (for Gray)

Though I intended to solve for t (time) and plug in t+11 to the coordinate equation:rcos(θ+pi), rsin(θ+pi)

Though I got lost on how to solve for the angle this time... which then gave me troubles finding time.

I knew that the angle had to be something like 2pi - θ at least... which just basically means the angle they swept through to meet the second time.

Anyway, what should I do from here? Unless there's another easier way.

Answers for the second part: (34.256, 16.898)

Thanks