A 40 inch board is cut into two pieces so that the shorter piece is two-thirds of the length of the longer piece. What are the lengths of the two cut pieces?

Please don't post a new question as a response to your own post. Often it would be overlooked since tutors think it has been answered.

1.
longer piece ---- x
shorter piece ----(2/3)x

x+ 2x/3 = 40
3x + 2x = 120
5x=120
x=24

long piece is 24 , short piece is 16

2. speed of plane in still air --- x mph
speed of wind ---- y mph

9(x-y) = 540 ---> x-y = 60
6(x+y) = 540 ---> x+y = 90

add them:
2x = 150
x = 75

speed of plane: 75 mph
speed of wind : 15 mph

traveling fromchicago to kansas city is a 540 mile trip. A small plane, facing a headwind (going against the wind), took 9 hours to get to kansas city. on the return trip to chicago the plane had a tailwind ( going with the wind) and the trip took only 6 hours. What was the average plane speed and the average wind speed?

_files/i0100000.jpg feet long. She needs to cut the board into 11 pieces of equal length. How long should each

Deb is slicing up a cake for three people. The cake is 45cm long and the second piece is 10cm longer than the first, and the third piece is 5 cm less than double the first . How big is each slice? What is the Algebra equation for this?

Write an algebraic expression to answer the question below.

A rope is cut into two pieces. One piece has a length of
72
inches. If the other piece has a length of
w
inches, what was the total length of the rope, in inches, before it was cut?

Well, isn't that a "length"y question. Let's bring out our mathematical scissors and get to work!

Let's call the length of the shorter piece "x". According to the information given, the longer piece must be two-thirds of the total length, which is 40 inches.

So, the longer piece would be (2/3) * 40 = 80/3 inches. Now, let's figure out the length of the shorter piece.

Since the shorter piece is two-thirds of the length of the longer piece, we can write the equation:

x = (2/3) * ((80/3) inches)

Now, let's grab our calculator... *beep boop beep* and simplify that.

x = 160/9 inches

So, the lengths of the two cut pieces are approximately 160/9 inches for the longer piece, and 2/3 of that for the shorter piece.

To solve this problem, we can set up an equation using the given information.

Let's assume the longer piece has a length of x inches. According to the problem, the shorter piece is two-thirds of the length of the longer piece.

So, the length of the shorter piece is (2/3) * x inches.

Now, we know that the sum of the lengths of the two pieces is equal to the original length of the board, which is 40 inches. Therefore, we can set up the equation:

x + (2/3) * x = 40

To solve the equation, we can combine like terms:

(5/3) * x = 40

Next, we will isolate x by multiplying both sides of the equation by 3/5:

(5/3) * x * (3/5) = 40 * (3/5)

Simplifying the equation further:

x = (120/5) = 24

Now, we have found the length of the longer piece, which is 24 inches. To find the length of the shorter piece, we can substitute this value back into our previous equation:

Length of shorter piece = (2/3) * x = (2/3) * 24 = 16

Therefore, the lengths of the two cut pieces are 24 inches and 16 inches, respectively.