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An empty water storage tank can be filled using two pumps, A and B. Pump A, working alone at its constant rate, takes x minutes to fill the tank. Pump B, working alone at its constant rate takes $$\frac{5}{4}$$ times as long as pump A to fill the tank. If it takes y minutes for pumps A and B, working simultaneously at their respective constant rates, to fill the tank, what is the ratio of x to y?

Give your answer as a fraction.
A tank initially contains $$g$$ gallons of water. Beginning at 1 o'clock in the afternoon, water flows into the top of the tank at a constant rate of $$x$$ gallons per minute and out of the bottom of the tank at a constant rate of $$y$$ gallons per minute. If $$ x \lt y$$, in how many minutes after 1 o'clock in the afternoon is the volume of water in the tank equal to $$\frac{1}{2}g$$, in terms of $$g$$, $$x$$, and $$y$$?
Water started running into an empty tank and continued running until it was filled to its capacity. Water ran at a constant rate of 200 kiloliters per minute for the first 20 minutes and then at a constant rate of 100 kiloliters per minute until the tank was filled. If it took a total of 80 minutes to fill the empty tank to its capacity, how many minutes did it take to fill the tank to $$\frac{1}{2}$$ of its capacity?

_____
A pump delivered water to fill an empty swimming pool. The pump delivered the water at a constant rate of 450 liters per minute until the pool was $$\frac{1}{2}$$ full. Then the pump became partially clogged and delivered the water at a slower constant rate until the pool was full. For the whole time during which the pump delivered water to fill the empty pool, its average rate was 360 liters per minute. What was the pump`s slower constant rate, in liters per minute?
If 40 units of water is discharged from a tank, then the water volume ratio in the tank will drop from $$\frac{1}{5}$$ to $$\frac{2}{11}$$. Next, if the tank needs to be filled with water, how many units of water need to be added to the tank?
When working at their respective rates, machine A produces 50 vases per hour and machine B produces 60 vases per hour.

Quantity A

The total number of vases machine A produces

Quantity B

The total number of vases machine B produces
A large pump and a small pump are available to fill a public fountain with 7,500 gallons of water. The pumps can be used alone or simultaneously. Working alone at their respective constant rates, the small pump would take 1.6 times as long as the large pump to fill the fountain. Working simultaneously at their respective constant rates, the two pumps would take 3 hours to fill the fountain. How long would the small pump take to fill the fountain, working alone at its constant rate?

_____hours
A certain machine devotes 45 seconds every 3 hours to a system check, and the machine is in operation 24 hours a day. At this rate, how many days of production will it take for the machine to spend a total of 3 hours on systems checks?
有一个监控路段长为1.5miles,限速是40miles/hour,某人开车匀速经过此路段花了108s.超速会被罚款,罚款规则是:只要超速就会罚款$50,然后超过40miles/hour的部分,每超过1mile/hour,就会罚$10,问一共罚了多少钱?
Pet drove a car 400 miles in 8 hours. For the first 6 hours, Pat drove on highway X; and the rest of the time, Pet drove on Highway Y. If the average speed for the car on highway X was 20 miles per hour more than the average speed on Highway Y, what was the car's average speed, in miles per hour, on highway Y?
On a trip, Marie drove the first half of the distance at an average speed of 30 miles per hour for a total of 13 hours of driving, and Juanita will drive the second half of the trip. They scheduled t hours driving for the entire distance. If they are to arrive exactly on schedule, at what average speed must Juanita drive the second half of the distance?
d=($$\frac{v_i+v_f)/}{2}$$)t

For an object that travels in a straight line with constant acceleration, the distance d that the object travels during time t is given by the formula shown, where v_i and v_f are the initial velocity and the final velocity of the object, respectively. A vehicle travelled distance of 32 kilometers along a straight route with constant acceleration. According to the formula, approximately how many minutes did it take the vehicle to travel the distance if the initial velocity and the final velocity of the vehicle were 14 meters per second and 20 meters per second, respectively?
An escalator installed at a new shopping mall operates at a speed of 90 feet per minute. The handrail of the escalator operates on a separate motor at a speed of 93 feet per minute. A person steps onto the escalator and, at the same time, grabs the handrail. Assuming that the person's hand and shoes do not move on the escalator in how many seconds will the person's hand have moved 0.25 foot more than the person's shoes?

_____seconds
A certain train travels 150 miles in h hours at the average rate of m miles per hour.

Quantity A

The number of hours required for the train to travel 320 miles at the average rate of 2m miles per hour

Quantity B

h
Last Saturday a cyclist started a 40-kilometer trip at 9 o`clock in the morning and rode at an average speed of 20 kilometers per hour for 45 minutes. The cyclist stopped to rest for x minutes and then rode at an average speed of 30 kilometers per hour until the trip was completed at 11 o`clock in the morning. What is the value of x?
In region A, 17 percent of the acres that are planted with corn are planted with a certain hybrid seed. In region B, which borders region A, 11 percent of the acres that are planted with corn are planted with the same hybrid seed.

Quantity A

Of all the acres planted with corn in region A and region B combined, the percent of acres that are planted with the hybrid seed

Quantity B

14%
$$r \gt s$$

List $$L$$ consists of $$r$$ values, and the average (arithmetic mean) of the values in $$L$$ is $$52.8$$. List $$M$$ consists of $$s$$ values, and the average of the values in $$M$$ is $$54.2$$. List $$K$$ consists of the values in $$L$$ and the values in $$M$$.

Quantity A

The average of the values in $$K$$

Quantity B

$$53.5$$
A certain charity is conducting a fund-raiser. For the first $9,000 raised by the charity, Company B will contribute $1 for every $3 collected by the charity. For any amount over $9,000 raised by the charity, Company B will contribute $2 for every $5 collected by the charity. How much money must the charity raise in order to reach a total of $68,000, including the contribution from Company B?
Company A and B earn commission fees based on their sales.



If company A sells $3,000, then how much does company B have to sell such that company B earns the same commission fee as company A?


Tickets for a carnival are sold either individually or in packages of 10 tickets or 20 tickets at the costs shown in the table. A group of friends bought $$n$$ tickets for the least possible total cost. A second group of friends bought more than $$n$$ tickets for a total cost that was less than the first group`s total cost. Which of the following could be the value of n?

Indicate all such values.

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