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Thus, in one single hour the smaller tube will fill part of the reservoir volume, while the larger tube will fill part of the reservoir volume in each single hour. Then the condition gives you this equation - = 1, (1) which is direct translation of the condition to Math.Working together, these two tubes will fill part of the reservoir volume in each single hour. If a beet-sugar factory in England processed 2000 tons less of beets per day, it would take 1 day longer to slice 60,000 tons of them. Solution Let x = "How many tons of beets are processed per day? To simplify calculations, we can make an agreement that we measure the amounts not in tons, but in THOUSANDS of tons. (2) You can solve the equation (2) formally by multiplying both sides by x: 60*x - 60*(x-2) = x*(x-2), 60x - 60x 120 = x^2 - 2x x^2 - 2x - 120 = 0 (x - 12)*(x 10) = 0.To simplify this equation, multiply both sides by , then transfer all terms from the right side to the left with the opposite signs, collect the common terms and adjust the signs. Solution Let be number of hours to fill the reservoir using the smaller tube only.
When you throw a ball (or shoot an arrow, fire a missile or throw a stone) it goes up into the air, slowing as it travels, then comes down again faster and faster ... and a Quadratic Equation tells you its position at all times! There are many ways to solve it, here we will factor it using the "Find two numbers that multiply to give a×c, and add to give b" method in Factoring Quadratics: a×c = A very profitable venture.
Your company is going to make frames as part of a new product they are launching.
This is the value of our „X“ and the solution of our word problem.
Knowing how to mathematically express and solve word problems has genuine real world applications and you will use those skills very often during the course of your everyday life.
One-step equations can also be communicated in the form of word problems.
The only difference between mathematically expressed equations and word problems is that, in word problems, you have to recognize the variable and other elements of the equation yourself.Therefore, it is important that you feel comfortable using them.To master solving word problems with one-step equations, download the worksheets below and practice solving them on your own.The easiest way to explain this would be using an example. Let us imagine that you are working as a computer programmer in a company that makes computer games.You are getting paid 50$ per hour and at the end of the day, you earned 400$.Working together, Andrew and Bill make of the whole work in each single day. The second root does not fit the given conditions: if Bill covers the roof in two days, then Andrew has 2-5=-3 days, which has no sense. The larger tube, if works separately, can fill the reservoir in 18 hours faster than the smaller tube.Since they can cover the entire roof in 6 days working together, the equation for the unknown value is as follows: . Apply the quadratic formula (see the lesson Introduction into Quadratic Equations) to solve this equation. So, the potentially correct solution is : Bill covers the roof in 15 days. If Bill gets the job done in 15 days, then Andrew makes it in 10 days, working separately. How long will it take to fill the reservoir using the smaller tube only?We can do that by dividing the whole equation by 50.50 * X = 400 |: 50 X = 8 You can see now that the number of hours you have to work to earn 400$ if you are being paid 50$ per hour is 8.Solution of quadratic equations is described in the lesson Introduction into Quadratic Equations in this module. Solution Let be the unknown current speed of the river in miles/hour.A motorboat makes a round trip on a river 56 miles upstream and 56 miles downstream, maintaining the constant speed 15 miles per hour relative to the water. When motorboat moves upstream, its speed relative to the bank of the river is miles/hour, and the time spent moving upstream is hours. For more examples of solved word problems of this type see the lesson Wind and Current problems solvable by quadratic equations under the topic Travel and Distance of the section Word problems in this site.