*Yes, this problem is a little trickier because the question is not asking for the maximum height (vertex) or the time it takes to reach the ground (zeros), instead it it asking for the time it takes to reach a height of 20 feet.*

I highly recommend the following textbook for both GCSE(9-1) and IGCSE(9-1).

The book covers every single topic in depth and offers plenty of questions to practise.

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.

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.However, these problems lead to quadratic equations. You can solve them by factoring or by using the Quadratic Formula. 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. Due to the nature of the mathematics on this site it is best views in landscape mode.If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width. Now you have to figure out what the problem even means before trying to solve it.There is enough coverage on new additions to the syllabus with a significant amount of questions.The following animation is interactive: by clicking on the button, you can generate a random equation and its solutions appear at the same time.Do you see how the ball will reach 20 feet on the way up and on the way down? We will now be solving for t using the quadratic formula. Our actual times were pretty close to our estimates.Just don't forget that when you solve a quadratic equation, you must have the equation set equal to 0.

## Comments Solving Problems With Quadratic Equations

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