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.

Question

(1 point)
Responses

2.5 miles
2.5 miles

1.2 miles
1.2 miles

4.2 miles
4.2 miles

1.8 miles

Answer 1

To determine how much distance Keith would have saved by riding directly to the pool, we can use the Pythagorean theorem.

Keith rode 3 miles down one road and then turned 90 degrees to ride another 3 miles. This forms a right triangle where both legs are 3 miles.

Using the Pythagorean theorem: \[ c = \sqrt{a^2 + b^2} \] where \( a \) and \( b \) are the lengths of the two legs (both are 3 miles), and \( c \) is the hypotenuse (the direct distance to the pool).

1. Calculate \( c \): \[ c = \sqrt{3^2 + 3^2} \] \[ c = \sqrt{9 + 9} \] \[ c = \sqrt{18} \] \[ c = 4.24264 \] miles (approximately)

2. Calculate the distance Keith actually rode: Keith rode 3 miles + 3 miles = 6 miles.

3. Calculate the distance saved: Distance saved = Distance rode - Direct distance \[ \text{Distance saved} = 6 \text{ miles} - 4.24264 \text{ miles} \] \[ \text{Distance saved} \approx 1.75736 \text{ miles} \]

Rounding to the nearest tenth, the distance saved is approximately 1.8 miles.

So the correct answer is 1.8 miles.