To find out how much distance Keith would have saved if he rode directly to the grocery store instead of taking the two 2-mile segments, we can use the Pythagorean theorem.
-
Keith traveled 2 miles down one road and then made a 90-degree turn and traveled another 2 miles down a different road. This forms a right triangle where each leg is 2 miles long.
-
According to the Pythagorean theorem, the distance \( d \) from his starting point (House) to the end point (Grocery Store) is given by: \[ d = \sqrt{(2 \text{ miles})^2 + (2 \text{ miles})^2} \] \[ d = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \text{ miles} \approx 2.83 \text{ miles} \]
-
Now, the total distance Keith rode is: \[ 2 \text{ miles} + 2 \text{ miles} = 4 \text{ miles} \]
-
To find how much distance he would have saved by riding directly to the store: \[ \text{savings} = \text{total distance ridden} - \text{direct distance} \] \[ \text{savings} = 4 \text{ miles} - 2.83 \text{ miles} \approx 1.17 \text{ miles} \]
Rounding to the nearest tenth, the distance saved is approximately 1.2 miles.
Therefore, the correct answer is 1.2 miles.
1 answer