A rope was cut in half. Half of the rope was cut in half again. After four such cuts, the length of one such rope was 1 m. What was the original length of the rope?
L * 1/2 *1/2 * 1/2 * 1/2 = L / 16
so
L/16 = 1
L = 16 meters
Let's start by calculating the length of the rope after each cut:
After the first cut, the rope was cut in half, so the length became 1m * 2 = 2m.
After the second cut, the rope was cut in half again, so the length became 2m * 2 = 4m.
After the third cut, the rope was cut in half again, so the length became 4m * 2 = 8m.
After the fourth cut, the rope was cut in half again, so the length became 8m * 2 = 16m.
Therefore, the original length of the rope must have been 16 meters.
To find the original length of the rope, we can work backwards from the given information. Let's start by denoting the original length of the rope as 'L'.
According to the problem, after the first cut, the length of one of the halves is equal to 1 meter. So, if "L" is the original length, then after the first cut, we have two halves of length L/2, and one of them is 1 meter long.
Now, after the second cut, one of the halves from the previous step is cut again. So, each of the resulting quarters will have a length of (L/2)/2 = L/4. We know that one of these quarters is 1 meter long.
Continuing the process, after the third cut, the length of each eighth will be (L/4)/2 = L/8. Similarly, after the fourth cut, the length of each sixteenth will be (L/8)/2 = L/16. And we are given that one of these sixteenths is 1 meter long.
Therefore, we can set up the equation to solve for the original length:
L/16 = 1
To isolate L, we can multiply both sides of the equation by 16:
L = 16
Therefore, the original length of the rope was 16 meters.