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

The rate is given by amount of probems over time.

To find the amount of problems done in a given amount of time, mulitply the rate by the given amount of time.

We can combine our y terms and cancel our n terms to simplify.

In this rate word problem, we need to find the rates at which Mary and Bejamin frost their respective cupcakes, and then sum their respective rates per hour. In one hour Mary frosts 133 cupcakes. (Note: the question specifies COMPLETELY frosted cupcakes only, so the fractional results here will need to be rounded down to the nearest integer.)  Benjamin frosts 82 cupcakes.

82 + 133=215

This problem states that John can paint a house in  hours. That means in  hour he will be able to paint  of a house.

The problem also states that Jill can paint a house in  hours. This means that in  hour, Jill can paint  of a house.

If they are painting together, you simply add the rate at which the paint separately together to find the rate at which they paint together. This means in  hour, they can paint  of a house. Now to find the time that paint an entire house, we simply invert that fraction, meaning that to paint an entire house together it would take them   of an hour, or .

The general formula for solving these work problems is , where  is the amount of time it takes worker A to finish the job alone and  is the amount of time it would take worker B to finish the job alone.