Directions: Solve the following problems dealing with rational expressions and/or equations. Only one solution method will be shown, but alternate solution methods are acceptable. Work carefully.

 1 Given parallelogram ABCD shown at the right. The area of ABCD is a2 + 2ab + b2 and AB = 3a + 3b. Find the height, h, in terms of a and b.

 2 Rate of discount, P, can be expressed as   where R = regular price and D is the discount (the amount saved off the regular price). a) Find the rate of discount on a skateboard which regularly sells for \$53.84 and is on sale for \$44.95. b) Solve the formula given above for R in terms of P and D.

 3 Given rectangle MATH shown at the right, with the length and height as labeled in terms of a and b. a) Express the perimeter of MATH in terms of a and b. b) Express the area of MATH in terms of a and b. You may assume that lengths are positive values.

 4 The sum of the reciprocals of two consecutive integers is . Find the two integers.

 5. Fred discovered that his large dog, Henry, can destroy his entire new Hosta garden in 1 hour, and that his small dog, Mandy, can do the same amount of destruction in 2 hours. How long would it take the two dogs working together to destroy the Hosta garden?

 6 Alana was visiting in a city 42 miles from her home. For the first 12 miles of her trip home, she was driving in a construction zone. When the construction zone ended, she was able to drive twice as fast for the remaining 30 miles. If the total trip took 1 hour, how fast was she driving in the construciton zone? You may assume a constant speed in each portion of her trip.

 7 An airplane can fly 910 miles with the wind in the same amount of time it takes for this same airplane to travel 660 miles against the wind. If the speed of the airplane in still-air is 305 miles per hour, what is the speed of the wind, in miles per hour?

 8 Working alone, it takes Simon 4 hours to paint the livingroom, while it takes Elaina 6 hours to paint the same room. How long will it take them to paint the livingroom together if Elaina leaves 2 hours early to pick up pizza?

 9 Jason is canoeing on a river that flows downstream at a rate of 1 mile per hour. After paddling 5 miles downstream, he turns around and paddles 6 miles upstream to report the condition of the river to the rest of his group. The trip takes 3 hours. How fast can Jason paddle in still water?

 10 Working alone, Joan can wash her car and clean the interior in one hour. If she enlists the help of her younger sister, Jackie, the car can be washed and cleaned in 40 minutes. How long will it take Jackie to wash the car and clean the interior if she works alone?