A baseball diamond is a square with sides 90 ft long. A batter is at bat, with runners at first and second base. At the moment the ball is hit, the runner at first base runs to second base at 25 ft/s. Simultaneously, the runner on second base runs to third base at 15 ft/s. How fast is the distance between these two runners changing 2 s after the ball is hit?

It is changing at -11 ft

Step-by-step explanation:

The distance d is given by

d = √x²+(90-y)²

We have to differentiate

dy/st = 25ft

dx/dt = -15ft

The question says after 2 seconds

Y = 25x2 = 50ft

X = -15x2 = -30ft

Then we calculate rate of change of distance. From the calculations I did, I arrived at

(1/2√900+1600).[900-2000]

= -1100/2x50

= -1100/100

= -11ft

Please check attachment to help you understand the answer better as it is more detailed.

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: