SOLUTION: There is a pole in a lake. One half of the pole is in the ground, another one third of it is covered with water, and 10ft is out of water. What is the total length of the pole in f

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Question 110465: There is a pole in a lake. One half of the pole is in the ground, another one third of it is covered with water, and 10ft is out of water. What is the total length of the pole in ft?
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Let x=length of pole in feet

So we know that half (1%2F2) of (which means "multiply") the pole (x) is in the ground. So %281%2F2%29x would be the expression for the length of the pole in the ground.

We also know that a third 1%2F3 of the pole is underwater. So %281%2F3%29x would be the expression for the length of the pole underwater.

Finally we know that 10 ft is above water. Now simply add all of the pieces of the pole to get the total length x

%281%2F2%29x%2B%281%2F3%29x%2B10=x this says that the sum of the parts equals the entire length of the pole


6%28%281%2F2%29x%2B%281%2F3%29x%2B10%29=6x Multiply both sides by the LCD 6 to remove the fractions


3x%2B2x%2B60=6x Distribute and multiply



5x%2B60=6x Combine like terms


cross%285x-5x%29%2B60=6x-5x Subtract 5x from both sides


60=x Combine like terms


So the length of the pole is 60 ft


Notice if we take half of 60, we get 30; if we take a third of 60, we get 20. Now add 30, 20 and 10 to get


30%2B20%2B10=60 So this verifies our answer.