Question

There is a pole in a lake. 1/2 of the pole is in the ground, another 1/3 of it is covered with water, and 10ft is out of water. What is the toal length of the pole in ft?

Answer 1

Step-by-step explanation:

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

Answer 2

Step-by-step explanation:

Let the total length of the pole be x ft.

Hence, part of the pole embedded in the ground = 1/2 × x = x/2 ft.

Part of the pole covered by water = 1/3 × x = x/3 ft.

Part of the pole out of water = 10 ft.

A/q,

x/2 + x/3 + 10 = x

( 3x + 2x )/6 + 10 = x

5x/6 + 10 = x

10 = x - 5x/6

10 = (6x - 5x)/6

10 = x/6

10 × 6 = x

x = 60

Now,

Total length of the pole

= x = 60 ft.

Part of the pole embedded in ground

= x/2 = 60/2 = 30 ft.

Part of the pole covered by water

= x/3 = 60/3 = 20 ft.

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