A reel of electric wire 150 metres long cut into two pieces. One is 40 metres shorter than twice the length of the other. How long is each piece.
Let one be x metres long
then the other is 150 - x
x+40 = 2(150-x)
x+40 = 300 - 2x
3x = 260
x = 260/3 m
one is 260/3 m, the other is 150-260/3 or 190/3 m
or in decimals, appr 86.67 m and 63.33 m.
check:
one is 86.67
twice the other is 126.67
which is 40 m more
Or, you can work it from the other side, which I find easier at the start:
x + 2x-40 = 150
3x = 190
x = 63.33
2x-40 = 126.67-40 = 86.67
To solve this problem, we can break down the information given and set up equations to find the lengths of the two pieces of wire.
Let's say the length of the first piece of wire is x meters. According to the problem, the other piece of wire is 40 meters shorter than twice the length of the first piece, so its length would be (2x - 40) meters.
We also know that the total length of the wire reel is 150 meters. Therefore, the sum of the lengths of the two pieces of wire should be equal to 150 meters.
So, we can write the equation:
x + (2x - 40) = 150
Now, let's solve the equation step by step:
Combine the like terms:
3x - 40 = 150
Add 40 to both sides of the equation:
3x = 190
Divide both sides of the equation by 3:
x = 190 / 3
Simplify the right side of the equation:
x ≈ 63.33
This means that the first piece of wire is approximately 63.33 meters long.
To find the length of the second piece, we can substitute the value of x back into (2x - 40):
(2 * 63.33) - 40 ≈ 126.66 - 40 ≈ 86.66
Therefore, the second piece of wire is approximately 86.66 meters long.
In conclusion, the first piece of wire is approximately 63.33 meters long, and the second piece is approximately 86.66 meters long.