Sylvia walked​ 3/4 ​mi east from her house to the bank. Then she walked 1/3 ​mi west to a gift shop. From the gift shop, she walked​ 1/4 ​mi west to a grocery store. How far is the grocery store from Sylvia's house?

Solution:The grocery store is 1/6 miles far from her house.Explanation:We have been given that Sylvia walked​ 3/4 ​mi east from her house to the bank. Hence, the distance between the house and the bank is 3/4 miles.Now, she walked 1/3 ​mi west to a gift shop. It means that she moved 1/3 miles towards her house. Also,  from the gift shop, she walked​ 1/4 ​mi west to a grocery store. It means she moved 1/3 miles plus 1/4 miles towards her house.Hence, the distance between the grocery store and the house is [tex]\frac{3}{4}-\left ( \frac{1}{3}+\frac{1}{4} \right )\\\\=\frac{3}{4}-\frac{1}{3}-\frac{1}{4} \\\\ =\frac{1}{6}[/tex]