To determine how much distance Keith would have saved by riding directly to the grocery store instead of following the two turns, we can use the Pythagorean theorem.
He rode 2 miles down one road and then took a 90-degree turn and rode another 2 miles down a different road. This forms a right triangle where the two legs are 2 miles each.
Using the Pythagorean theorem: \[ c = \sqrt{a^2 + b^2} \] where \(a\) and \(b\) are the lengths of the two legs of the triangle (both 2 miles).
Calculating: \[ c = \sqrt{2^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} \approx 2.83 \text{ miles} \]
Now, the total distance Keith rode following the two paths is: \[ 2 \text{ miles} + 2 \text{ miles} = 4 \text{ miles} \]
To find out how much distance he would have saved, we subtract the direct distance from the total distance he rode: \[ \text{Distance saved} = 4 \text{ miles} - 2.83 \text{ miles} \approx 1.17 \text{ miles} \] Rounding to the nearest tenth: \[ \text{Distance saved} \approx 1.2 \text{ miles} \]
Thus, the answer is 1.2 miles.
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