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

Answer 1

Answer:

1 1/4

Explanation:

Find the length of the diagonal of the rectangle to find the length of the direct line to the starting time using Pythagorean Theorem.

1 1/4

heh, not a really good explanation but at least it's correct XD

Answer 2

Explanation:

The attached figure shows the whole description.

Fraction covered in south, $x_1=\dfrac{1}{2}$

Fraction covered in east, $x_2=\dfrac{3}{4}$

Fraction covered in south, $x_3=\dfrac{1}{2}$

MNO is a right angle triangle.

$MO^2=MN^2+NO^2$

$MO^2=(3/8)^2+(1/2)^2$

$MO=0.62\ mile$

So, $AM=2\times MO$

$AM=2\times 0.62$

AM = 1.24 miles

So, he is 1.24 miles from his starting point. Hence, this is the required solution.