A carpenter drills 5 equally spaced holes in a 56 3/4" long piece of wood. The two end holes are an equal distance from the center. If each hole is 7 1/2 inches apart, what is the distance from each end of the wood to the nearest ens hole?
Please explain
Thanks,
Mark
If each of 5 equally-spaced holes is 7.5 inches apart and one hole is in the center, the end holes are 15" from the center. Thus the middle 30" is between these holes. Therefore, 56.75 - 30 gives you the distance from both end holes to the end of the wood.
Do you think you can take it from there?
I hope this helps. Thanks for asking.
To solve this problem, let's break it down into steps:
Step 1: Determine the length of the spaces between the holes:
A carpenter drills 5 equally spaced holes in a 56 3/4" long piece of wood. If there are 5 holes, there will be 4 spaces between them. To find the length of each space, we need to subtract the combined length of the 5 holes from the total length of the wood.
Total length of the wood = 56 3/4"
Number of spaces = 4
Length of each space = (56 3/4") / 4
Step 2: Determine the distance from the center to the nearest end hole:
The problem states that the two end holes are an equal distance from the center. This means that the length from the center to the nearest end hole will be half the length of each space between the holes.
Distance from center to nearest end hole = (Length of each space) / 2
Step 3: Calculate the final answer:
By following the steps above, we can determine the distance from each end of the wood to the nearest end hole:
Distance from each end of the wood to the nearest end hole = Distance from center to nearest end hole + Length of each space
Now, let's calculate each step:
Step 1:
Total length of the wood = 56 3/4"
Number of spaces = 4
Length of each space = (56 3/4") / 4 = 14 3/8"
Step 2:
Distance from center to nearest end hole = (Length of each space) / 2 = (14 3/8") / 2 = 7 3/16"
Step 3:
Distance from each end of the wood to the nearest end hole = Distance from center to nearest end hole + Length of each space
= 7 3/16" + 14 3/8"
= 7 3/16" + 14 3/8"
= 21 9/16"
Therefore, the distance from each end of the wood to the nearest end hole is 21 9/16".