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 4.2 miles 4.2 miles 2.5 miles

Answer 1

To find out how much distance Keith would have saved by riding directly to the pool instead of following the two roads, we can visualize the situation as a right triangle.

In this triangle:
- One leg of the triangle is 3 miles (the distance he rode straight down the first road).
- The other leg of the triangle is also 3 miles (the distance he rode down the second road after the turn).

We can use the Pythagorean theorem to find the length of the hypotenuse (the direct distance to the pool):

\[
c = \sqrt{a^2 + b^2}
\]

where:
- \( a = 3 \) miles (first leg)
- \( b = 3 \) miles (second leg)

Calculating the hypotenuse:

\[
c = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} \approx 4.24 \text{ miles}
\]

Keith traveled a total of:

\[
3 + 3 = 6 \text{ miles}
\]

Now, to find out how much distance he could have saved by riding directly to the pool:

\[
\text{Distance saved} = \text{Distance traveled} - \text{Direct distance} = 6 - 4.24 \approx 1.76 \text{ miles}
\]

Rounding this to the nearest tenth gives:

**1.8 miles**

So the answer is **1.8 miles**.