a 45 inch rope is cut into 3 pieces. the first piece of rope is 3 inches longer than the other pieces of rope. what is the length of the longest piece of rope.

17 in

To find the length of the longest piece of rope, we can start by setting up an equation based on the given information.

Let's assume the length of the shortest piece of rope is x inches. Since the first piece of rope is 3 inches longer than the other pieces, the length of the first piece can be expressed as (x + 3) inches.

Now, we have two pieces of rope with lengths x inches and one piece with (x + 3) inches. The total length of the three pieces of rope is 45 inches.

So, we can write the equation:

x + x + x + 3 = 45

Simplifying this equation, we get:

3x + 3 = 45

Subtracting 3 from both sides, we have:

3x = 42

Dividing both sides by 3:

x = 14

Now that we know the length of the shortest piece of rope, we can find the length of the longest piece by substituting the value of x back into our assumption.

The length of the longest piece of rope is:

14 + 3 = 17 inches