To find the distance we would use the pythagorean theorem and solve for z. x= 10(Pedro's distance) and y = 15(queen's distance).

x

^{2}+ y

^{2}= z

^{2}

10

^{2}+ 15

^{2}= z

^{2}

To find the rate of change of z we have to differentiate x

^{2}+ y

^{2}= z

^{2}.

x(dx/dt) + y(dy/dt) = z(dz/dt)

before we plug in our given values we have to convert the units. I decided to convert m/s to km/hr.

(1.38m/s)(3.6) = 5 km/hr

(2.22m/s)(3.6) = 8 km/hr

Now we can plug in the values.

x(dx/dt) + y(dy/dt) = z(dz/dt)

(10)(5) + (15)(8) =

170 /

dz/dt = 9.4299 km/hr

If you convert that to m/s you can divide the answer by 3.6

9.4299 / 3.6 = 2.62 m/s