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).

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).
Transcript text: 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).
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Solution

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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 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 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.

Step 1: Inequality for Manuel's Exercise

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

Step 2: Inequality for the Bullet Train's Cruising Speed

For the bullet train's cruising speed, which is stated to be no less than 130 miles per hour, we define the variable s 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: s130 s \geq 130

Final Answer

The inequalities representing the situations are: t>50 \boxed{t > 50} s130 \boxed{s \geq 130}

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