To find the distance Keith would have saved by going directly to the pool instead of his bike route, we can use the Pythagorean theorem.
He rode 3 miles down one road and then took a 90-degree turn and rode another 3 miles down a different road. The path he took creates a right triangle where:
- One leg of the triangle is 3 miles (the first segment),
- The other leg is also 3 miles (the second segment).
According to the Pythagorean theorem:
\[ c = \sqrt{a^2 + b^2} \]
where \(a\) and \(b\) are the lengths of the legs of the triangle, and \(c\) is the length of the hypotenuse (the direct distance to the pool).
Substituting the values we have:
\[ c = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} \approx 4.2426 \]
Rounding this to the nearest tenth, we find:
\[ c \approx 4.2 \text{ miles} \]
Now, to find the distance Keith actually rode, we add the two segments:
\[ 3 \text{ miles} + 3 \text{ miles} = 6 \text{ miles} \]
Finally, the distance saved by riding directly to the pool would be the difference between the distance he actually rode and the direct distance:
\[ \text{Distance saved} = 6 \text{ miles} - 4.2 \text{ miles} = 1.8 \text{ miles} \]
So, rounding to the nearest tenth, Keith saved 1.8 miles.
The correct response is:
1.8 miles