SOLUTION: A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward first base with a speed of 22 ft/s. At what rate is his distance from second b

This is a related-rates problem.



The distance h from the runner to 2nd base is 

where x is the remaining distance from the runner to 1st base.



Given:

 but note that because the way I've defined x, it is decreasing.  Therefore I will write  so if we get a negative answer it indicates a decreasing distance. 



[ If you instead insist on dx/dt > 0, you can say dx/dt=22 ft/s and define x as the distance from home plate to the runner, then the distance remaining to first base is 90-x and you end up with the minus sign later, but the math is a little uglier. ]



Using the chain rule:

 = 



Plugging in x=45 gives   ft/s

 (The runner's distance with respect to 2nd base is decreasing at 9.839 ft/s)