1)
Rational Equation Applications Name:________________________
Analysis BC
Not Calculator Active. Set up an equation and solve without using your calculator.
1) The denominator of a fraction is 3 less than twice the numerator. When the numerator is increased by 8 and the denominator by 35, the resulting fraction is 1/3. Find the fraction.
2) An airplane has enough fuel for a safe flying time of 88 minutes. Its air speed flying east is 300km/h and returning is 250km/h. How far east may it be flown?
3) Two people can complete a task in 2 2/3 days when they work together. Working alone one person takes 4 days more than the other. Find the number of days it takes each to complete the task.
4) A mixing vat can be filled by 2 pipes in 4hr and 5hr, respectively, and can be emptied by a third pipe in 6hr. How many hours will it take to fill the mixing vat when all the pipes are used.
5) When 260 is divided by a certain number, the quotient is 15 and the remainder is 5. Find the number.
6) A bus travels east for 250km and then heads north 352km. Its rate going north is 6km/h less than its rate going east. When the total time for the trip is 13 hours, find the speed of the bus going east.
Calculator Active. Set up an equation in terms of x and use your calculator to find the max/min value.
7) A right triangle is formed in the first quadrant by the x-axis, y-axis and a line segment through the point (3, 2). Find the value of a that yields a minimum area and find the area. (Hint: use similar triangles to find an equation for y).
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8) A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of the page are 1.5 inches wide. The margins on each side are 1 inch. What should the dimensions of the page be so that the least amount of paper is used?
9) A cylindrical can of food contains a volume of 14.5 cubic inches. How should the can be constructed so that the material made to make the can is a minimum?
10) A farmer plans to fence a rectangular pasture adjacent to a river. The pasture must contain 180,000 square meters in order to provide enough grass for the herd. What dimensions would require the least amount of fencing if no fencing is needed along the river?
Answers:
1) 8/13 2) 200km 3) 4 & 8 days 4) 3 9/17hrs 5) 17
6) 50km/h 7) a = 6, A = 12 8) 6 in by 9 in 9) r = 1.321in, h = 2.643 in
10) 300 ft by 600 ft
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