Question

To determine 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.

Keith rode 3 miles down one road and then took a 90-degree turn and rode another 3 miles. This forms a right triangle where each leg of the triangle is 3 miles long.

Let's denote the distances as follows:
- One leg (first road) = 3 miles
- Second leg (second road) = 3 miles

Using the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
where:
- \(c\) is the hypotenuse (direct distance to the pool),
- \(a = 3\) miles,
- \(b = 3\) miles.

Calculating \(c\):
\[
c = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2} \approx 4.2426 \text{ miles}
\]

Now, Keith rode a total of:
\[
3 \text{ miles} + 3 \text{ miles} = 6 \text{ miles}
\]

To find out how much distance he would have saved, we subtract the direct distance from the total distance ridden:
\[
\text{Distance Saved} = 6 \text{ miles} - 4.2426 \text{ miles} \approx 1.7574 \text{ miles}
\]

Rounding this to the nearest tenth gives us approximately **1.8 miles**.

Thus, the answer is:
**1.8 miles**