a board is 17ft long and a hole is 1 ft futher from 1 end than it is from the other. How far is the hole from each end of the board shortest distance? Choices 6,8,10
How did you get 8?
Half of 17 = 8 1/2
So the hole must be 8 feet from one end and 9 feet from the other end.
Thank you... I did not realize how easy that was.
You're welcome. :-)
To find the shortest distance of the hole from each end of the board, we can use the concept of symmetry.
Let's assume that the distance from one end to the hole is x ft. Since the hole is 1 ft further from one end than it is from the other, the distance from the other end to the hole would be x + 1 ft.
Given that the total length of the board is 17 ft, we can sum up the distances from both ends to the hole:
x + (x + 1) = 17
By simplifying, we get:
2x + 1 = 17
Subtracting 1 from both sides:
2x = 16
Dividing both sides by 2:
x = 8
So, the distance from one end to the hole is 8 ft, and the distance from the other end to the hole would be 8 + 1 = 9 ft.
Therefore, the shortest distance of the hole from each end of the board is 8 ft and 9 ft, respectively.
So, the correct answer would be 8 and 9.