# algebra

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?

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1. 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?

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2. 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

2x = 150
x = 75

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

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3. black people eat chicken

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

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5. 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?

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6. 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?

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