Quadratic word problems

The square of a number is decreased by 15. This value is twice the original number. Find the number(s).

One number is the square of another. Their sum is 132. Find the numbers.

A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What will be the width of the pathway?

A square and rectangle have the same area. The length of the rectangle is five inches more than twice the length of the side of the square. The width of the rectangle is 6 inches less than the side of the square. Find the length of the side of the square.

You have a 500-foot roll of fencing and a large field. You want to construct a rectangular playground area. What are the dimensions of the largest such yard? What is the largest area?

Your company is going to make frames as part of a new product they are launching.
The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be 28 cm2 The inside of the frame has to be 11 cm by 6 cm What should the width of the metal be?

A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an hour. What is the boat's speed and how long was the upstream journey?

The difference of two numbers is 2 and their product is 224. Find the numbers.

The area of a rectangle is 560 square inches. The length is 3 more than twice the width. Find the length and the width.

Calvin and Bonzo can eat 1260 hamburgers in 12 hours. Eating by himself, it would take Calvin 7 hours longer to eat 1260 hamburgers than it would take Bonzo to eat 1260 hamburgers. How long would it take Bonzo to eat 1260 hamburgers by himself?

If Calvin and Bonzo eat together, they can eat 480 hot dogs in 6 hours.Eating alone, Bonzo takes 16 hours longer than Calvin would to eat 480 hot dogs.How long does it take Calvin to eat 480 hot dogs?

Calvin rides his power boat up and down a drainage ditch. The water in the drainage ditch flows at 6 miles per hour. Calvin takes 5 hours longer to travel 360 miles against the current than he does to travel 360 miles with the current. What is the speed of Calvin's boat in still water?

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.The entire trip up and back takes 7.5 hours.
What is the speed of the current?

Andrew and Bill, working together, can cover the roof of a house in 6 days. Andrew, working alone, can complete this job in 5 days less than Bill. How long will it take Bill to make this job?

Two tubes, working together, can fill the reservoir with the liquid in 12 hours. The larger tube, if works separately, can fill the reservoir in 18 hours less than the smaller tube. How long will it take to fill the reservoir using the smaller tube only?

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