A football player took forward and backward steps of equal length during a play. After taking 14 steps total, he was back at his starting position. How many steps did the football player take in the forward and backward directions?
(1 point)
Group of answer choices
6 steps forward and 8 steps backward
7 steps forward and 7 steps backward
8 steps forward and 6 steps backward
5 steps forward and 9 steps backward
Let's assume the number of steps the player took forward is x. Since the player took an equal number of forward and backward steps, the number of steps the player took backward is also x.
The total number of steps taken by the player is 14. So, we have the equation:
x + x = 14
Simplifying the equation, we get:
2x = 14
Dividing both sides of the equation by 2, we get:
x = 7
Therefore, the player took 7 steps forward and 7 steps backward.
Thus, the correct answer is: 7 steps forward and 7 steps backward.
Let's solve this step by step.
Let's assume that the number of forward steps the football player took is 'F', and the number of backward steps is 'B'.
According to the given information, the football player took a total of 14 steps. So we have the equation:
F + B = 14 (Equation 1)
We are also given that after taking these steps, the football player ended up back at his starting position. This means that the total displacement should be zero. Since each forward step and each backward step are of equal length, the displacement for each step cancels out.
The displacement for the forward steps is F, and the displacement for the backward steps is -B (negative B because it is in the opposite direction). So, the equation for the displacement becomes:
F - B = 0 (Equation 2)
Now we have a system of equations with two variables (F and B). We can solve this system by eliminating one of the variables.
Adding Equation 1 and Equation 2, we get:
(F + B) + (F - B) = 14 + 0
2F = 14
F = 14/2
F = 7
Substituting the value of F into Equation 1, we can find the value of B:
7 + B = 14
B = 14 - 7
B = 7
Therefore, the football player took 7 steps forward and 7 steps backward.
The correct answer is:
7 steps forward and 7 steps backward.
To solve this question, we need to divide the total number of steps (14) evenly between the forward and backward directions. Since the football player took an equal number of steps in both directions, we can divide 14 by 2 to get the number of steps in each direction.
14 / 2 = 7
Therefore, the football player took 7 steps in both the forward and backward directions.
So, the correct answer is:
7 steps forward and 7 steps backward.