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.

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

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.

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

First we determine how many gallons it will take to travel 3,149 miles with this particular car: 3,149/31=101.58 gallons. The cost of gas per gallon= $3.69, therefore 101.58x$3.69= $374.83.

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

First, we need to convert the 1 hour into minutes in order to keep consistent with units -- so, the car averages 32 miles per 60 minutes.  Then, a ratio can be set up to solve this: 32 mi / 60 min = x mi / 20 min. Cross multiplying and dividing, we get x = 10.667 miles.  Rounding to the nearest tenth, this becomes 10.7 miles. 

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