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题目内容
Helen and Sergey must cut down a row of trees. Helen can cut down the entire row in 3 hours, and Sergey can cut down the entire row in 7 hours. If they simultaneously start cutting trees, each starting at one end of the row and working towards each other, what fraction of the trees will Sergey have cut at the time they meet?_____
In a set of five consecutive integers, which of the following must change the average of the set without changing its original median ?
Paul is able to grade p essays every half hour, and Sarah is able to grade s essays every hour. If Paul and Sarah work together grading essays for h hours, then in terms of p, s, and h, how many essays will they grade?Indicate all such amounts.
If the average of 5 numbers is 36 and the average of four of those numbers is 34, then what is the value of the fifth number?
Noah`s contracting company builds road at a rate of 1 mile per week, except during the rainy season, when that rate drops to $$\frac{1}{2}$$ mile per week. If Noah is hired to build 11 miles of road, and his company begins construction 5 weeks before the start of the rainy season, how many weeks will it take Noah`s company to complete the contract? (Rainy season lasts 14 weeks.)_____
Two cyclists, A and B, are 145 miles apart on a straight road. At 1:30 p.m., cyclist A begins riding at a constant speed of 20 miles per hour toward cyclist B. At 2:00 p.m., cyclist B begins riding toward cyclist A at a constant speed. At 5:00 p.m. they meet. How fast, in miles per hour, was cyclist B riding?_____
Portia rates all her first dates as either "duds" or "dudes." Her date on Wednesday night was a dud. On the next night, she went on a date with someone else who was also a dud. If the probability of her getting two duds in a row was $$\frac{4}{25}$$, what is the probability that her next date will be a dude ?
Victor is walking at a rate of 1 mile every 17 minutes. Sarah is walking at a rate of 1 mile every 14 minutes. If they are 10 miles apart and are approaching each other along a straight road, how many hours will it take them to meet, rounded to the nearest hundredth?_____

Quantity A

(3p+1)(3p-1)

Quantity B

$$9p^{2}$$
a > 0

Quantity A

(a + 2)(3a + 6)

Quantity B

(3a + 2)(a + 6)

Quantity A

$$3^{2}-2^{2}$$

Quantity B

$$(3-2)(3+2)$$
If $$(2x+2)^2=0$$, then x =_____
a > 0

Quantity A

(–a – 10)(10 + a)

Quantity B

10
(y – 1)(y + 5) = 0

Quantity A

y

Quantity B

3
If m > 0 and $$3m^2$$ + 12m – 15 = 0, then m =_____
If the difference between two numbers is 4, then which of the following would be sufficient to determine the value of each of the numbers?Indicate all possible values.
A rectangle is formed by increasing two opposite sides of a square of side length x by y units, and decreasing the two remaining sides of the square by y units. What is the area of the rectangle?
The net profit that Ann makes from selling x pillows is given by the expression $$x^{2} – 2x – 288.$$

Quantity A

The number of pillows that Ann must sell for her net profit to be zero

Quantity B

20
What is the greatest value of x for which (3x – 2)(x + 1) = 0 ?
$$x^{2}=y^{2}+1$$ and $${y}\neq{0}$$

Quantity A

$$x^{4}$$

Quantity B

$$y^{4}+1$$

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