Questions: Write inequalities to represent the situations below. Manuel exercises more than 50 minutes per day. Use t to represent Manuel's amount of exercise (in minutes per day). The cruising speed of the bullet train will be no less than 130 miles per hour. Use s to represent the train's cruising speed (in miles per hour).

Solution Steps

To solve these problems, we need to translate the given real-world situations into mathematical inequalities using the specified variables.

1. For the first situation, "Manuel exercises more than 50 minutes per day," we use the variable \( t \) to represent the amount of exercise in minutes. The phrase "more than" indicates a strict inequality.

2. For the second situation, "The cruising speed of the bullet train will be no less than 130 miles per hour," we use the variable \( s \) to represent the train's cruising speed. The phrase "no less than" indicates that the speed is at least 130 miles per hour, which translates to a greater than or equal to inequality.

To represent the situation where Manuel exercises more than 50 minutes per day, we define the variable \( t \) as the amount of exercise in minutes. The phrase "more than" translates to the inequality: \[ t > 50 \]

For the bullet train's cruising speed, which is stated to be no less than 130 miles per hour, we define the variable \( s \) as the train's cruising speed in miles per hour. The phrase "no less than" indicates that the speed is at least 130 miles per hour, leading to the inequality: \[ s \geq 130 \]

Final Answer