Question

You and some friends are trapped inside a rectangular room that is leaking water from the ceiling filling up the room with water. Picking up a small cubic gift box (6 inches in length) you time the box fills in exactly 3 minutes. While you were timing the filling of the box, your friends measured the room to be 10 feet x 12 feet x 8 feet . Assuming no water is seeping out of the room, determine how fast the water level in the room is rising the moment the water in the room is 5 feet deep. Your shortest friend stands 5' 8". Give them the sad news of how much longer they have before they are completely submerged in water.

Answer 1

Volume of the small cubic gift box (6 inches in length) = 63 = 216 cubic inches.

Since the box fills in exactly 3 minutes, so in 1 minute water fiiled 216/3 = 72 cubic inches.

Let at the moment the water in the room is 5 feet deep, water level in the room is rising by h inches/minute.

Now lenght of the room = 10 feet = 10×12 inches and width of the room = 12 feet = 12×12 inches.

Thus, (10×12)×(12×12)×h = 72

   ⇒ h = 1/240

Hence the water level in the room is rising by 1/240 inches/minute.

At the moment the water in the room is 5 feet deep, to completely submerge your shortest friend of height 5'8'', the water should rised by (5'8''-5')=8 inches in the room.

So to rise the water level by 8 inches it take 8×240 minutes = 8×4 hours = 32 hours.

Hence they 32 hours have before they are completely submerged in water.