Question

Bill walks $\frac{1}{2}$ mile south, then $\frac{3}{4}$ mile east, and finally $\frac{1}{2}$ mile south. How many miles is he, in a direct line, from his starting point?

$1$

$1 \frac{1}{4}$

$1 \frac{1}{2}$

$1 \frac{3}{4}$

$2$

Answer: B

Concepts:Pythagorean Theorem fraction

Difficulty rating: 940

Solution:

Note that what we want is the length of the diagonal. We can use the Pythagorean theorem to find this. $\sqrt{\left(\dfrac{1}{2} + \dfrac{1}{2}\right)^2 + \dfrac{3}{4}^2}$ $= \sqrt{1 + \dfrac{9}{16}} = \sqrt{\dfrac{25}{16}} = \dfrac{5}{4}$

Thus, B is the correct answer.

2005 AMC 8 Problem 7

Answer: B

Difficulty rating: 940

Solution:

Problem 7 in Other Years