Question
Keith left his house for the pool. He rode his bike 3 miles down one road, took a 90-degree turn, and rode another 3 miles down a different road before arriving at the pool. If he had ridden directly to the pool, how much distance would he have saved? Round your answer to the nearest tenth.(1 point)Responses4.2 miles4.2 miles2.5 miles2.5 miles1.8 miles1.8 miles1.2 miles
Answers
GPT-4o mini
To find the distance Keith would have saved if he rode directly to the pool instead of taking the two roads, 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. This forms a right triangle where each leg is 3 miles.
The formula for the hypotenuse \(c\) in a right triangle is:
\[
c = \sqrt{a^2 + b^2}
\]
Where \(a\) and \(b\) are the lengths of the legs. In this case:
\[
a = 3 \text{ miles}, \quad b = 3 \text{ miles}
\]
Substituting in the values, we have:
\[
c = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}
\]
Calculating \(3\sqrt{2}\):
\[
3\sqrt{2} \approx 3 \times 1.414 \approx 4.242 \text{ miles}
\]
Now, we can find the distance he saved by subtracting the direct distance from the total distance he rode:
- Total distance he rode: \(3 + 3 = 6\) miles.
- Direct distance to the pool: \(4.242\) miles.
Distance saved:
\[
6 - 4.242 \approx 1.758 \text{ miles}
\]
Rounding to the nearest tenth:
\[
\approx 1.8 \text{ miles}
\]
Therefore, the distance he would have saved is **1.8 miles**.
He 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 is 3 miles.
The formula for the hypotenuse \(c\) in a right triangle is:
\[
c = \sqrt{a^2 + b^2}
\]
Where \(a\) and \(b\) are the lengths of the legs. In this case:
\[
a = 3 \text{ miles}, \quad b = 3 \text{ miles}
\]
Substituting in the values, we have:
\[
c = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}
\]
Calculating \(3\sqrt{2}\):
\[
3\sqrt{2} \approx 3 \times 1.414 \approx 4.242 \text{ miles}
\]
Now, we can find the distance he saved by subtracting the direct distance from the total distance he rode:
- Total distance he rode: \(3 + 3 = 6\) miles.
- Direct distance to the pool: \(4.242\) miles.
Distance saved:
\[
6 - 4.242 \approx 1.758 \text{ miles}
\]
Rounding to the nearest tenth:
\[
\approx 1.8 \text{ miles}
\]
Therefore, the distance he would have saved is **1.8 miles**.