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 .

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).

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 .

To calculate miles per gallon of gas, we take the 478 miles the motorcycle travels and divide it by the amount of gallons in a full tank of gas, 12 gallons. 478/12 = 39.83, or 39.8 when rounded to the tenths place

For the price, we take the 12 gallons and multiply it by the amount that one gallon costs, $4.25. (12)(4.25) = 51

We divide 1,457 miles by 47 miles per gallon to find that 31 gallons of gas are needed for the road trip.

We then multiply the gallons of gas by the cost per gallon to find:

31 x 4.13 = 128.03

Begin by setting up the standard equation

However, for our data, we know the distance and the rate only. We do not know the time that it took for the person's return. It is , where is the return time. Thus, we can write:

Solving for , we get:

, which rounds to minutes.

In general for work problems: W1 + W2 = 1 where Work = Rate x Time

Note, 1 represents the completed job assignment.

For example, W1 is the rate that the first person would finish the job multiplied by the time it would take two or more people to finish the job completely.

1/3x + 1/2x = 1 where x is the time it would take for both people to complete the job.

Find a common denominator to add the fractions, then solve for x.

x = 1.2 days for one house, but the questions asks about two houses, so the correct answer is 2.4 days.

Remember that distance = rate x time

For the first route, we can set up an equation where the total distance (36 + 44) equals the rate (65 mph) multiplied by the time:

36 +44 = 65t

80 = 65t

t = 80/65 = 1.23 hrs = 1 hr, 14 min

To find the time taken for the second route, we first figure out the distance traveled by using the Pythagorean Theorem.

We know that the "legs" of the right triangle are 44 and 36, where the hypotenuse is the straightline distance (northwest), directly to the destination:

a2+b2=c2

442+362=c2

3232=c2

c=56.85

56.85=40t

56.85/40=t

t=1.42 hrs=1 hr, 25 min

1 hr. 25 min. – 1 hr. 14 min. = 11 min.

Property area = 10,000 ft x 40,000 ft = 400,000,000 ft2

Acreage = 400,000,000 ft2 / 43,560 ft2 per acre = 9,183 acres

Taxes = $3.50 per acre x 9,183 acres = $32,140

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.