Question

You will cut two boards (exactly the same length after the cut) and place them end to end. Suppose the combined length must be within 0.06 inch of 30 inches. Then each board must be within how many inches of 15?

Select one:

a. If each board is within 15.03 inches distance of 15 inches, then the combined length of the boards is within 0.06 inch of 30 inches.

b. If each board is within 14.97 inches distance of 15 inches, then the combined length of the boards is within 0.06 inch of 30 inches.

c. If each board is within 15 inches distance of 15 inches, then the combined length of the boards is within 0.06 inch of 30 inches.

d. If each board is within 0.03 inch distance of 15 inches, then the combined length of the boards is within 0.06 inch of 30 inches.

Answer 1

The length of each board is expressed as 15+h where h is tiny.

The length of two boards is 2(15+h)=30+k where k is the discrepancy in the total length.

So 30+2h=30+k making 2h=k. We are told k=0.06 in, so h=0.06/2=0.03 in.

This means the length of each board must be within 0.03 in of 15 in, answer choice d.