Jacob and Ali want to run from one corner of a football field to the opposite corner. The rectangular football field is 50 yards
wide and 120 yards long. Jacob runs around the perimeter of the field, while Ali runs in a straight line through the middle of the field. How many more yards does Jacob run than Ali?
1 answer:
Answer:
Jacob ran 40 yards more than Ali.
Step-by-step explanation:
Football field is in the shape of a rectangle having dimensions 120 yards × 50 yards
Since Jacob runs around the perimeter of the field from one corner to other corner, therefore, distance run by Jacob =
Distance run by Jacob = 50 + 120 = 170 yards
Ali runs through the middle of the field diagonally on a straight line.
Therefore, distance covered by Ali =
=
=
=
= 130 yards
Now difference between the distance covered by Jacob and Ali
= 170 - 130
= 40 yards
Therefore, Jacob ran 40 yards more than Ali.
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1. Using a graphing calculator.
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By ordering this equation we have:
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Thus, by plotting this function, we have that the graph of this function is indicated in Figure 1. By zooming, we can see, in Figure 2, that the roots of the polynomial equation are the x-intercepts of which are:
Finally, rounding noninteger roots to the nearest hundredth we have:
2. Using a system of equations.
The ordered equation is:
By arranging to factor out we have:
Then, by factoring:
Term is a common factor, thus:
