Hello, jsu03!

I hope you had a good diagram.

1. A baseball diamond is a square with sides 90 ft. At the moment a batter hits the ball,

a runner from first base starts running to second base with a speed of 22 ft/sec

and a runner from second base starts running to third base with a speed of 28 ft/sec.

At what rate is the distance between these two runners changing 1 second later?

Is this distance increasing or decreasing? Code:

C
y *
D * * 90-x
o * B
* o
* * x
* *
* * A
* *
* *
* *
* *
* *
*

At time , the runner on 1st has run feet from

. . where ft/sec. .Note that:

At the same time, the runner on 2nd has run feet from

. . where ft/sec.

Draw line segment , and let

Since is a right triangle: .

Differentiate with respect to time: .

. . and we have: . .[1]

When

. . and: .

Substitute into [1]: .

Therefore: .