The cold-water faucet fills the bucket in 30 minutes, so in 1 minute it fills 1/30 of the bucket. The hot-water faucet fills the bucket in 60 minutes, so in 1 minute it fills 1/60 of the bucket. Then, when they're both running together they fill 1/30 + 1/60 of the bucket in 1 minute.  

1/30 + 1/60 = 2/60 + 1/60 = 3/60 = 1/20, so they fill the whole bucket in 20 minutes. 

The puppy starts at 4 pounds and gains 1 pound per month for 8 months, so he weighs 4 + 8 = 12 pounds at the end of 8 months. The kitten starts at 2 pounds and gains 2 pounds per month for 7 months, so he weighs 2 + 14 = 16 pounds at the end of 7 months. Therefore Quantity B is greater.

It's tempting to take the two rates and average them. This is wrong but the GRE will always give you this as a trap answer choice. In this problem, looking at the two rates separately would give us 40 mi/hr and 20 mi/hr, making the trap answer here 30 mi/hr.  

The key is that Kathy goes 40 mi/hr for 1 hour and then 20 mi/hr for 3 hours, so the speed should be less than the middle number of 30. 18 mi/hr is lower than her lowest speed so that doesn't make sense, and 20 mi/hr is too low because the 1 hour at 40 mi/hr should bring the average up a little bit. Therefore the answer must be 25 mi/hr.

We can also do the computations to find the answer. The correct formula is average miles per hour = total miles / total hours.  Plugging in our values, average speed = (40 + 60) miles / (1 + 3) hours = 25 mi/hr.

This problem gives the rate of Hose A instead of the time it takes to fill the shark tank. Let's convert the rest of the problem information into rates as well.  The tank is 10,000 gallons, and it takes the two hoses together 4 hours to fill the tank.  Therefore, the combined rate is 10,000/4 = 2,500 gallons per hour.

Now we know that Hose A can deliver 1,000 gallons in an hour, and together Hose A and Hose B can deliver 2,500 gallons in an hour.  So 1,000 gallons + Hose B gallons = 2,500 gallons.  Then Hose B fills the tank at 2500 – 1000 = 1500 gallons/hour.

The change in temperature is 100 – 65 = 35 degrees. The change in time is 9 AM to 2 PM, or 5 hours. So the rate of change is 35 degrees / 5 hours = 7 degrees / hour.

Ben mows 1 lawn in 1 hour, or 1/60 of the lawn in 1 minute. Ken mows 1 lawn in 2 hours, or 1/120 of the lawn in 1 minute. Then each minute they mow 1/60 + 1/120 = 3/120 = 1/40 of the lawn. That means the entire lawn takes 40 minutes to mow.

First, we must determine how many feet per hour the train travels.

50 feet per second * 60 seconds in a minute * 60 minutes in an hour.

50 * 60 * 60 = 180,000

Then, it's just a matter of converting 180,000 feet to miles.  Because there are 5280 feet in a mile, just divide.

180,000 / 5280 = 34.091

First find what fraction of the job is completed per hour. If John can paint the room in 4 hours, then he completes  of it per hour. Similarly, Susan paints  of it per hour. So together they paint  of the room per hour. 

Add  by rewriting them with the same common denominator (least common multiple of 4 and 6 is 12, so 12 is the least common denominator):

This means  of the job is completed per hour. To find the number of hours for the whole job (1 room), divide the whole by the fraction completed per hour:

Convert hours to minutes:

If Carol ate 3 pancakes in 5 minutes, she can eat  of a pancake every minute. .

That means she ate 14 whole pancakes (and an additional 2/5 of another pancake).

Approach this problem with the following reasoning.

Unit of work done = number of workers * rate * time

In our case, we are given 24 "workers," able to make 5 "units of work," in 0.5 "time." The rate is not given, but can be solved for with our given information.

Units of work = 5

Number of workers = 24

Time = 0.5 hours (30 minutes)

Now, since we know the rate, which does not chage, we can solve for the new time when the number of machines is decreased and the number of devices is increased.

 Unit of work done = number of workers * rate * time