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
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