SOLUTION: A rectangular airport runway is x feet long and y feet wide. If its length is to be made 100 feet longer, by how many square feet will its area be increased?

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Question 1208792: A rectangular airport runway is x feet long and y feet wide. If its length is to be made 100 feet longer, by how many square feet will its area be increased?


Found 3 solutions by ikleyn, math_tutor2020, MathTherapy:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

The area of the runway will increase by 100*y square feet,

and this increment does not depend on x.


=========================


Comment from student:   Why does the increment not depend on x?


My response:   Extremely stupid question.

You may be surprised, but there is no need to ask "why" - Because it is obvious.


......................................


When a person feigns a desire to solve a math problem, but his brain is sleeping,
it is an unresolvable internal contradiction of things. These conceptions are not compatible.


\\\\\\\\\\\\\\\\\\\\\\\\\\\\\


        To the next generation of students who will read this post.


The problem in the post is, on the one hand, a joke, and on the other hand, a test.

It is a test to see if a person, who solves it, can immediately grasp the core of the problem
to solve it with the minimum amount of time and efforts/calculations,
and, in general, to see if the interviewed person is inclined to look for effective thinking/solving.

The other tutors began to make completely unnecessary calculations, determining the area
of ​​the original runway and the area of the updated runway, and then calculating the difference.

While the simplest calculation is one single multiplication of the width by the increment of the length.

Again, it is a typical test to see if the examinee sees the core of the problem and strives
to solve it with the least amount of time and efforts, by the most effective way.

When and if you will be in the similar situation on the test, remember this.


        Actually, this test is very effective.

        Indeed, it produces the outcome instantly;
        from the other side hand, the interviewed person does not even realize
        and does not even suspect that his hidden qualities are being tested here.



Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!


The original runway is the rectangle on the left.
The added part is the rectangle on the right which has an area of 100*y square feet.
For example, if y = 15 then 100*y = 100*15 = 1500 square feet has been added.
But since we don't know the value of y, we leave the expression 100y as it is.

Answer: 100y
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
A rectangular airport runway is x feet long and y feet wide. If its length is to be made 100 feet longer, by how many square feet will its area be increased?

With length and width being x and y, respectively, ORIGINAL area = xy
WIth length increasing by 100, NEW length becomes: x + 100
As width (y) remains constant, NEW area = (x + 100)y = xy + 100y

Comparing OLD area, xy to NEW area, xy + 100y, we see that the increase in area is 100y (NEW area - OLD area = xy + 100y - xy).
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