Rebecca, Justin, and Robert are trapped in a rectangular room 8 feet deep and 10 feet tall. Two opposing walls are closing in at a rate of 1 foot per minute. If the water in the room is 2 feet deep when the moving walls are 12 feet apart, how fast is the water level rising when it reaches the top of Justin’s head, if Justin is 6 feet tall?

Question

Please show and explain ALL work. Thank you.

Answer 1

so, let the width of the room be x feet. So, at time t,
x = 12-2t
If the height of the water is h, then the volume of water is
v = 8xh
dv/dt = 8h dx/dt + 8x dh/dt = 0
So now plug in your numbers to find dh/dt when h=6

Answer 2

I still don’t understand what numbers to plug in.