Alfi Blog

Alfi Blog

Alfi Blog


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Distance Problems

Distance Problems

 

There are several distance problems that quadratic equations can solve. One of these types is ‘‘stream’’ problems: a vehicle travels the same distance up and back where in one direction, the ‘‘stream’s’’ average speed is added to the vehicle’s speed and in the other, the ‘‘stream’s’’ average speed is subtracted from the vehicle’s speed. Another type involves two bodies moving away from each other where their paths form a right angle (for instance, one travels north and the other west). Finally, the last type is where a vehicle makes a round trip that takes longer in one direction than in the other. In all of these types, the formula D = RT is key.

Geometric Problems - 1

Examples

 

The area of a triangle is 40 in2. Its height is four-fifths the length of its base. What are its base and height?

   The area is 40 and H = B so the formula A = ½ BH becomes 40 = ½ B(B).

Geometric Problems

Geometric Problems

 

To solve word problems involving geometric shapes, write down the formula or formulas referred to in the problem. For example, after reading ‘‘The perimeter of a rectangular room . . . ’’ write P = 2L + 2W. Then fill in the information given about the formula. For example, after reading ‘‘The peri- meter of the room is 50 feet . . . ’’ write P = 50 and 50 = 2L + 2W. ‘‘Its width is two-thirds its length.’’ Write W = L and 50 = 2L + 2W becomes 50 = 2L + 2( L).

The Height of a Falling Object - 2

Examples

 

An object is tossed up in the air at the rate of 40 feet per second. How long will it take for the object to hit the ground?

The Height of a Falling Object - 1

Example

 

An object is dropped from the roof of a 60-foot building. How longbmust it fall to reach a height of 28 feet?

   In the formula h = 16t2 + v0t + h0, h0 is 60 and v0 is zero (because the object is dropped). The object reaches a height of 28 feet when h = 28.

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