# Word Problem Involving the Rate of Filling or Emptying a Rectangular Prism

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In this lesson we solve word problems involving the rate of filling or emptying a rectangular prism.

Formula to find time to drain or fill up a rectangular prism at a certain rate.

If the rate of filling up or draining a rectangular prism is ‘r’ units per minute and if the volume of the prism is ‘V’ cubic units, then the time taken is given by

Time taken to drain/fill up = Volume/ rate = V/r

Stacy is cleaning out her fish tank that is 6 feet long, 4 feet wide, and 3 feet deep. It is 70% full of water and drains at the rate of 2 cubic foot per minute. How long does it take to drain completely?

### Solution

Step 1:

Volume of water = 0.7 × 6ft × 4ft × 3ft

= 50.4 cu ft

Step 2:

Time taken to drain = Volume/rate = 50.4/2

= 25.2 minutes

A rectangular water tank 8 m × 1.8 m × 3.5 m is 1/5 full of water. How long does it take to fill the tank completely, if it fills up at the rate of 2 kilolitres per minute?

### Solution

Step 1:

Volume of water to fill = 4/5 × 8.0 m × 1.8 m × 3.5 m

= 40.32 cu m

Step 2:

Time taken to fill up = Volume/rate = 40.32/2

= 20.16 minutes