Question

in a woodworking shop, you are planing boards to make shelves. the planer is set to remove $\frac{1}{10}$ inch from a board on each pass the board makes through the planer. if a board starts out at $\frac{3}{4}$ inch thick, how many times will you need to send it through the planer to get it down to $\frac{5}{8}$ inch?

a. 2
b. 3
c. 4
d. 8
e. 16

Explanation:

Step1: Find the amount to be removed

Let the number of passes be $n$. The amount removed per pass is $\frac{1}{10}$ inch. The initial thickness is $\frac{3}{4}$ inch and the final thickness is $\frac{5}{8}$ inch. The amount to be removed is $\frac{3}{4}-\frac{5}{8}$.
We find a common - denominator: $\frac{3}{4}-\frac{5}{8}=\frac{6}{8}-\frac{5}{8}=\frac{6 - 5}{8}=\frac{1}{8}$ inch.

Step2: Set up an equation

Since the amount removed per pass is $\frac{1}{10}$ inch and the total amount to be removed is $\frac{1}{8}$ inch, we have the equation $\frac{1}{10}n=\frac{1}{8}$.

Step3: Solve for $n$

Cross - multiply: $8n = 10$. Then $n=\frac{10}{8}=\frac{5}{4}=1.25$. But since we can't have a fraction of a pass and we need to reach at least $\frac{5}{8}$ inch, we consider the next whole number. If we do 1 pass, the remaining thickness is $\frac{3}{4}-\frac{1}{10}=\frac{15 - 2}{20}=\frac{13}{20}=0.65$ inch. If we do 2 passes, the remaining thickness is $\frac{3}{4}-2\times\frac{1}{10}=\frac{3}{4}-\frac{1}{5}=\frac{15 - 4}{20}=\frac{11}{20}=0.55$ inch which is less than $\frac{5}{8}=0.625$ inch. So we need 2 passes.

Answer:

A. 2