Question

Lucy is running a test on her car engine that requires her to be moving. The tolerance for variation in her car's speed, in miles/hour, while tuning the test is given the inequality |x - 60| ≤ 3. Assume x is the actual speed of the car at any time during the test. What is the minimum acceptable speed? What is the maximum acceptable speed?

A) Minimum acceptable speed: 57 miles/hour, Maximum acceptable speed: 63 miles/hour
B) Minimum acceptable speed: 60 miles/hour, Maximum acceptable speed: 63 miles/hour
C) Minimum acceptable speed: 57 miles/hour, Maximum acceptable speed: 60 miles/hour
D) Minimum acceptable speed: 60 miles/hour, Maximum acceptable speed: 66 miles/hour

Answer 1

Lucy's car must maintain a speed within the range specified by the inequality |x - 60| ≤ 3. Solving this inequality, the minimum acceptable speed is 57 mph, and the maximum acceptable speed is 63 mph. Therefore, the correct answer is A.

Step-by-step explanation:

The inequality |x - 60| ≤ 3 describes a range of speeds where x is the speed of Lucy's car. This inequality can be understood as the car's speed being within 3 miles per hour of 60 mph. To solve for the minimum and maximum acceptable speeds, the inequality is broken into two separate conditions: x - 60 ≤ 3 and -(x - 60) ≤ 3 (or 60 - x ≤ 3).

For the first condition, solving x - 60 ≤ 3 gives us x ≤ 63. This means that the maximum acceptable speed is 63 mph.

For the second condition, solving 60 - x ≤ 3 gives us x ≥ 57. This indicates that the minimum acceptable speed is 57 mph.

Therefore, the acceptable range of speeds for Lucy's car during the test is from 57 mph to 63 mph. Answer choice A is correct: Minimum acceptable speed: 57 miles/hour, Maximum acceptable speed: 63 miles/hour.