# Problem Solving With Quadratics Thesis Mechanics

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 quadratic formula to find the roots, x = [-b ± √(b 2x-6 = 0 Here, a = 1, b=2 and c= -6. → x = [-2 ± √(4*7)] / 2 → x = [-2 ± 2√7] / 2 → x = 2[ -1 ± √7] / 2 → x = -1 ± √7 Hence, √7-1 and -√7-1 are the roots of this equation. Solve for x: x 10x-24 = 0 What are the two numbers which when added give 10 and when multiplied give -24? Substituting these values in the formula, x = [-2 ± √(4 – (4*1*-6))] / 2*1 → x = [-2 ± √(4 24)] / 2 → x = [-2 ± √28] / 2 When we get a non-perfect square in a square root, we usually try to express it as a product of two numbers in which one is a perfect square. The first sentence says one is the square of the other, so I can write The sum is 132, so Plug into and solve for B: The possible solutions are and .

I completely understand and here's where I am going to try to help!

However, these problems lead to quadratic equations.

You can solve them by factoring or by using the Quadratic Formula.

There are many types of problems that can easily be solved using your knowledge of quadratic equations.

You may come across problems that deal with money and predicted incomes (financial) or problems that deal with physics such as projectiles.

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