First, find the total amount of gas necessary for the trip. 6363/63 = 101 gallons (easy to see as 63 * 100 = 6300 + 1 * 63 = 6363). Then multiply the number of gallons by the price per gallon of gasoline, 5.05 * 101 = $510.05 and is your answer (again, easy to see when 5.05 * 100 + 1 * 5.05).

Remember that distance/time=rate, so then:

x/15 = 65

x = 65 * 15

x = 975 miles

The general equation is distance = rate x time.  In addition, the distance upstream is the same as the distance downstream.  So, r_up x t_up = r_down x t_down.  Be sure to convert minutes to hours because the rate is given in mph (miles per hour).

Therefore, (r + 3)(1/2) = (r – 3)(1) and solve for r.

Note, r + 3 is the downstream rate and r – 3 is the upstream rate

In order to get the total amount of gas used in Sarah’s trip, first find how much gas was used on the highway and add it to the amount used in the city. Highway gas usage can be found by dividing

 and city usage can be found by dividing

.

Then we add these two answers together and get  

We know that the rate of a car can be written in the equation:

This means that you need the distance and time of your total trip. We know that the trip was a total of  or  hours. The distance is easily calculated by multiplying each respective rate by its number of hours, thus, you know:

Therefore, you know that the rate of the total trip was:

Recall that the basic form for a rate is:

, where  is generically the amount of work done. Since the question asks for the answer in gallons per hour, you should start by changing your time amount into hours. This is done by multiplying  by  to get .

Thus, we know:

The rate of draining is  once the new pipe is added. Recall that:

, where  is the total work output. For our data, this means the total amount of water. Now, we are measuring our rate in hours, so we should translate the three days' time into hours. This is easily done:

Now, based on this, we can set up the equation:

Now, this means that there will be  or  gallons in the reservoir after three days.

This problem is a variation on the standard equation .  The  variable contains all twenty bakers, however, instead of just one.  Still, let's start by substituting in our data:

Solving for , we get .

Now, this represents how many dozen cookies the whole group of  make per hour.  We can find the individual rate by dividing  by , which gives us .  Notice, however, that the question asks for the number of cookies—not the number of dozens.  Therefore, you need to multiply  by , which gives you .

This problem is a variation on the standard equation .  The  variable contains all the workers.  Therefore, we could rewrite this as , where  is the number of workers and  is the individual rate of work.  Thus, for our first bit of data, we know:

Solving for , you get 

Now, for the actual question, we can fill out the complete equation based on this data:

Solving for , you get .

Recall that in general 

Now, let's gather our three rates:

Rate 1: 

Rate 2: 

Rate 3: 

Now, we know that the time is a total of  hours.  Based on our data, we can write:

This is  miles per hour, which rounds to .