Question

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)
Responses

1.2 miles
1.2 miles

1.8 miles
1.8 miles

2.5 miles
2.5 miles

4.2 miles
4.2 miles

Answer 1

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**