To find out how much distance Keith would have saved by riding directly to the pool instead of taking the two roads, we can use the Pythagorean theorem.
When Keith rode 3 miles down one road and then took a 90-degree turn to ride another 3 miles down a different road, he essentially formed a right triangle. The two legs of the triangle (the two segments he rode) are both 3 miles long. The distance he would have saved is the length of the hypotenuse of this right triangle.
According to the Pythagorean theorem:
\[ c = \sqrt{a^2 + b^2} \]
where \(a\) and \(b\) are the legs of the triangle and \(c\) is the hypotenuse.
In this case:
\[ a = 3 \text{ miles} \] \[ b = 3 \text{ miles} \]
Now we'll calculate the hypotenuse \(c\):
\[ c = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2} \approx 4.2426 \text{ miles} \]
Now, we can determine how much distance he rode compared to the direct route:
Distance rode = \(3 + 3 = 6\) miles.
Distance saved = Distance rode - Direct distance: \[ \text{Distance saved} = 6 - c \approx 6 - 4.2426 \approx 1.7574 \text{ miles} \]
Rounding this to the nearest tenth, we get:
\[ \text{Distance saved} \approx 1.8 \text{ miles} \]
Thus, Keith would have saved approximately 1.8 miles by riding directly to the pool.