Richard needs to fly from san diego to halifax, nova scotia and back in order to give an important talk about mathematics. on the way to halifax, he will get a speed boost from the wind which blows at 50 miles per hour (mph). on the way back, the plane must, unfortunately, fight this wind speed. if the talk lasts 2 hours, and if the distance between the two cities is 3000 miles, how fast must the plane fly in mph if the entire trip is to take 13 hours?

When plane is going towards Halifax the speed of wind is in the direction of fly

so overall the net speed of the plane will increase

while when he is on the way back the air is opposite to flight so net speed will decrease

now the total time of the journey is 13 hours

out of this 2 hours he spent in mathematics talk

so total time of the fly is 13 - 2 = 11 hours

now we have formula to find the time to travel to Halinex

time taken to reach back

now we have total time

here d= 3000 miles

solving above quadratic equation we will have

so speed of plane will be 550 mph

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.