Question

A pole of height 3 metres is stuck by a speeding car and breaks into two pieces such that the first piece is $\dfrac{1}{2}$ of the second. Find the length of both pieces.

Answer 1

Hint: We first assume the length of the pieces of the pole. We find the total which is equal to 3 and then solve the equation to find the solution of the variable.

Complete step by step solution:
A pole of height 3 metres is stuck by a speeding car and breaks into two pieces such that the first piece is $\dfrac{1}{2}$ of the second.
Let us assume the length of the first piece as $x$ metres. It is given that the first piece is $\dfrac{1}{2}$ of the second which means the second piece is twice the first.
Therefore, the length of the second piece is $2x$ metres.
The total of these two pieces will be $2x+x=3x$ meters.
Now we equate it with a total length of 3 metres to find the equation of $3x=3$.
Dividing both sides with 3 we get $\dfrac{3x}{3}=\dfrac{3}{3}\Rightarrow x=1$.
Therefore, the length of the first piece is 1 meter. The length of the second piece is 2 meters.

Note:
We also could have taken the length of the second piece as $x$ to find the length of the first piece to be $\dfrac{x}{2}$. The inverse relation will also give the same result.