The following table shows the amount of work done by each pump during the hour when they are both working.

The total work done by both pumps in an hour is:

The remaining work to be completed by the slowest pump is:

The time taken by the slowest pump to complete filling the pool is the quotient of the remaining work by the work rate of the slowest pump:

It will take the slowest pump 7/2 hours to complete filling the pool.

All five workers have the same work rate, therefore they all complete an equal portion of the work done. Each worker's rate is:

Each worker can then classify 50 files in a day.

To classify 1250 files, the company therefore needs the following number of temporary workers:

Twenty-five workers are needed to classify the 1250 files in a day.

Let  be the number of hours it took to fill the tank.

The inlet pipe takes three hours to fill the tank, so it can fill  tank in one hour, and  tank in  hours.

The drain can empty the tank in five hours, so it can remove  tank in one hour; since it started two hours after the filling started, it worked for  hours to empty  tank worth of water.

The work performed by the drain was against that performed by the inlet pipe, so the difference of their results is one tank of water. Therefore, the equation to solve for  is

Let  be the amount of time it would take for Phillip to paint the house by himself. Then he can paint  of a house per hour. Similarly, since Bryan can paint the house by himself in 25 hours, he can paint  of the house per hour. 

Since the two brothers together paint one house in 16 hours, Bryan's share of the work is to paint  of one house. Phillip's share of the work is to paint  of the house. Their shares together add up to one house, so the problem to be solved is

Cross-multiply and solve:

 hours.

Of the given choices, 45 hours comes closest.

Let  be the number of hours it took to fill the tank.

The inlet pipe takes  hours to fill the tank, so it fills  tank per hour. The drain empties the tank in  hours, so it empties  tank per hour. In  hours, the inlet pipe filled  tanks of water, but the drain let out  tanks of water; the one tank of water was the difference of these amounts, so

This makes 9 hours the correct response.

Let  be the number of hours it takes the three koala bears together to eat the leaves. Then Stuffy can eat the leaves in  hours, Fluffy can eat them in  hours, and Muffy can eat them in 24 hours. Therefore, in one hour, Stuffy, Fluffy, and Muffy can eat , , and  of the leaves, respectively, and in  hours, Stuffy can eat  of the leaves, Fluffy can eat  of the leaves, and Muffy can eat  of the leaves. Since together they are eating all of the leaves, the sum of the three amounts is one task, so we solve for  in the equation:

It takes 10 hours for all three koalas together to eat all the leaves on Mr. Meany's farm.

To begin, convert minutes to hours for each project.

Notebook Cover: 

   Samuel is making thirteen of these, so we need to multiply the result by thirteen.  is the amount of time Samuel needs to make thirteen notebook covers.

Book Cover: 

   Samuel is making three times as many book covers as he is making notebook covers. , so he is making  book covers.

It will take Samuel  to make  book covers.

Add up the calculated times to get the total number of hours it will take Samuel to make the given number of notebook covers and book covers:

. That's almost a full work-week of work!

To solve this problem, we need to set up an equation as follows

,.

 is Mary's rate.

By simply manipulating the terms, we end up with

 , which is the final answer.

The first machine can make ; this is

 doughnuts per minute.

Similarly, the second machine can make ; this is

 doughnuts per minute.

Working together, the machines make 

doughnuts per minute, or, equivalently, .

.

Let  be the amount of time it takes for the second crew to paint a house without the first.

Think of this as a rate problem, with rate being measured in "houses per hour" rather than "hours per house". The first crew alone can paint  house per hour; the second alone can paint  house per hour; both together can paint  house per hour.

We can find the portion of the house each crew does in an amount of time by multiplying its rate in house per hour by the time in hourse elapsed.

Let's look at what happens when the two crews are working together over five hours, adding their efforts:

or

The third house will be painted in about 8.6 hours.