Solving Quadratic Problems

However, these problems lead to quadratic equations.

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How long would it take Bonzo to eat 1260 hamburgers by himself? Calvin takes 5 hours longer to travel 360 miles against the current than he does to travel 360 miles with the current. Let x be the speed of Calvin's boat in miles per hour in still water, and let t be the time in hours it takes him to travel 360 miles with the current.

Eating by himself, it would take Calvin 7 hours longer to eat 1260 hamburgers than it would take Bonzo to eat 1260 hamburgers. The last equation gives The second equation gives Plug into : Plug into the first equation and solve for t: The solution doesn't make sense, since time can't be negative. Eating alone, Bonzo takes 16 hours longer than Calvin would to eat 480 hot dogs. Let x be Calvin's rate (in hot dogs per hour), let y be Bonzo's rate, and let t be the time it takes Calvin to eat 480 hot dogs. The water in the drainage ditch flows at 6 miles per hour.

The equations are Solve the second equation for t: Plug this into the first equation and solve for x: The solutions are .

Thus, it takes him hours to travel 360 miles against the current.

Console yourself with the knowledge that you're not likely ever to need this skill in real life.

These word problems involve situations I've discussed in other word problems: The area of a rectangle, motion (time, speed, and distance), and work. Our approach combines a semidefinite relaxation with a cutting plane technique, and is applied in a Branch and Bound setting. Our experiments indicate that this type of approach is very robust, and allows to solve many moderately sized problems, having say, less than 100 binary variables, in a routine manner. When you use the Principle of Zero Products to solve a quadratic equation, you need to make sure that the equation is equal to zero.For example, 12x 10m as 2m(m 5) and then set the factors equal to 0.This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness.Together, they cited information from 7 references. The length is 3 more than twice the width, so The area is 560, so Plug in and solve for W: Use the Quadratic Formula: Since the width can't be negative, I get . Calvin and Bonzo can eat 1260 hamburgers in 12 hours. If Calvin and Bonzo eat together, they can eat 480 hot dogs in 6 hours. Plug these into the first equation and solve for t: The solutions are and . Calvin rides his power boat up and down a drainage ditch.Many word problems Involving unknown quantities can be translated for solving quadratic equations Methods of solving quadratic equations are discussed here in the following steps. Step II: use the conditions of the problem to establish in unknown quantities.The two values that we found via factoring, x = −4 and x = 3, lead to true statements: 0 = 0. But x = 5, the value not found by factoring, creates an untrue statement—27 does not equal 0!Note in the example above, if the common factor of 2 had been factored out, the resulting factor would be (−r 3), which is the negative of (r – 3).

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