A time study was conducted to determine the length of time required to perform a task in a manufacturing process. The times required by approximately two-thirds of the workers in the study satisfied the inequality $∣t−15.61.6∣≤1\left| \frac { t - 15.6 } { 1.6 } \right| \leq 1$ where t is the time in minutes. What are the maximum and minimum times? Round your answer to one decimal place.

A) minimum time is $14$ minutes, maximum time is $15.6$ minutes
B) minimum time is $14$ minutes, maximum time is $17.2$ minutes
C) minimum time is $14$ minutes, maximum time is $17.9$ minutes
D) minimum time is $15.6$ minutes, maximum time is $17.2$ minutes
E) minimum time is $13.5$ minutes, maximum time is $17.2$ minutes

Question

A time study was conducted to determine the length of time required to perform a task in a manufacturing process. The times required by approximately two-thirds of the workers in the study satisfied the inequality

∣t−15.61.6∣≤1\left| \frac { t - 15.6 } { 1.6 } \right| \leq 1

where t is the time in minutes. What are the maximum and minimum times? Round your answer to one decimal place.

A) minimum time is

14

minutes, maximum time is

15.6

minutes
B) minimum time is

14

minutes, maximum time is

17.2

minutes
C) minimum time is

14

minutes, maximum time is

17.9

minutes
D) minimum time is

15.6

minutes, maximum time is

17.2

minutes
E) minimum time is

13.5

minutes, maximum time is

17.2

minutes

classic margarita · Accepted Answer

Final Answer : B, Explanation :   Solving the inequality   ∣ t − 15.6 1.6 ∣ ≤ 1 \left| \frac { t - 15.6 } { 1.6 } \right| \leq 1 ​ 1.6 t − 15.6 ​ ​ ≤ 1   gives us two inequalities:   t − 15.6 1.6 ≤ 1  \frac { t - 15.6 } { 1.6 } \leq 1 1.6 t − 15.6 ​ ≤ 1   and   t − 15.6 1.6 ≥ − 1  \frac { t - 15.6 } { 1.6 } \geq -1 1.6 t − 15.6 ​ ≥ − 1  . Solving these gives   t ≤ 17.2 t \leq 17.2 t ≤ 17.2   and   t ≥ 14 t \geq 14 t ≥ 14  , respectively. Therefore, the minimum time is 14 minutes and the maximum time is 17.2 minutes.

Definitions

Learning Objectives

Learning Objectives

Related questions