A water tower is a structure that holds water in a tank, high off the ground.An old water tower had a weakness in one of its supporting beams. As the tank was filled, a beam at the building's foundation started to bend. For every 16 gallons of water, the beam bends 3 cm from its normal position.If the tank contains 384 pints of water, how much will the beam have bent?
Question
A water tower is a structure that holds water in a tank, high off the ground.An old water tower had a weakness in one of its supporting beams. As the tank was filled, a beam at the building's foundation started to bend. For every 16 gallons of water, the beam bends 3 cm from its normal position.If the tank contains 384 pints of water, how much will the beam have bent?
Solution
First, we need to convert the volume of water from pints to gallons because the rate of bending is given in gallons. There are 8 pints in a gallon. So, 384 pints is equal to 384/8 = 48 gallons.
Next, we know that for every 16 gallons of water, the beam bends 3 cm. So, for 48 gallons of water, we need to find out how much the beam will bend.
We can set up a proportion to solve this: 16 gallons/3 cm = 48 gallons/x cm.
Cross-multiplying gives us 16x = 144.
Solving for x, we get x = 144/16 = 9 cm.
So, the beam will have bent 9 cm.
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