A stick 42 inches long is broken into 2 pieces, so that one piece is twice as long as the other. How long are the two pieces?
Let x be the length of the shorter piece.
Then the longer piece is 2x.
The sum of the two pieces is x + 2x = 3x.
Since the stick is 42 inches long, we have:
3x = 42
x = 14
Therefore, the shorter piece is 14 inches long, and the longer piece is 2x = 28 inches long.
Two rectangles have the same width. One is 12 units long, and one is 8 units long. If one is 320 square units longer that the other, then what is the width of each?
Let's call the common width of the rectangles "w". We know that the area of the first rectangle is length times width, or 12w. Similarly, the area of the second rectangle is 8w.
We are told that one rectangle is 320 square units bigger than the other. This can be written as an equation:
12w - 8w = 320
Simplifying, we get:
4w = 320
Dividing both sides by 4, we find that:
w = 80
So the width of each rectangle is 80 units.
max sneezes every 5 minutes. lina coughs every 6 minutes. doggie barks every three minutes. if there was sneezing, barking and coughing at 3:15 PM, what time will these sounds happen simultaneously again?
In order for all three actions to happen simultaneously again, we need to find the smallest common multiple of 5, 6, and 3 (in minutes).
The prime factorization of 5 is just 5.
The prime factorization of 6 is 2 x 3.
The prime factorization of 3 is just 3.
To find the smallest common multiple, we first take the highest power of each prime factor that appears in any of the three factorizations. In this case, that would be 2 x 3 x 5, since 2 is the highest power of 2 that appears, 3 is the highest power of 3, and 5 is the highest power of 5.
Multiplying these three numbers together, we get:
2 x 3 x 5 = 30
Therefore, all three actions (sneezing, coughing, and barking) will happen simultaneously again every 30 minutes. If the sounds occurred at 3:15 PM, they will happen together again at 3:15 + 0:30 = 3:45 PM.
Let's assume the length of the shorter piece is "x" inches. Since the longer piece is twice as long, its length will be "2x" inches.
According to the given information, the sum of the lengths of the two pieces should equal the total length of the stick, which is 42 inches.
So, our equation becomes:
x + 2x = 42
Combining like terms, we have:
3x = 42
To isolate x, we divide both sides of the equation by 3:
x = 42 / 3
Simplifying further:
x = 14
Therefore, the shorter piece is 14 inches long, and the longer piece is twice as long, making it 2 * 14 = 28 inches long.
To solve this problem, we can set up an equation based on the given information.
Let's say the length of the shorter piece is x inches. According to the problem, the longer piece is twice as long as the shorter piece. Therefore, the length of the longer piece would be 2x inches.
Since the total length of the stick is 42 inches, we can write the equation:
x + 2x = 42
Now we can solve for x:
3x = 42
Dividing both sides of the equation by 3:
x = 14
So, the length of the shorter piece is 14 inches. And since the longer piece is twice as long, the length of the longer piece is 2 * 14 = 28 inches.
Therefore, the two pieces are 14 inches and 28 inches long, respectively.