Answer :
Certainly! Let's go through the problem step by step.
The problem states:
Dan was riding in a bicycle race. After the first five hours of racing, he had ridden more than 175 km. We need to express this situation using a mathematical sentence where [tex]\( s \)[/tex] represents the variable "average speed."
Step 1: Understanding the Concept of Average Speed
The formula for average speed [tex]\( s \)[/tex] is given by:
[tex]\[ s = \frac{\text{Total Distance}}{\text{Total Time}} \][/tex]
Step 2: Applying the Problem's Data
From the problem, we know:
- Total Distance is more than 175 km.
- Total Time is 5 hours.
Step 3: Setting Up the Inequality
Since [tex]\( s \)[/tex] represents the average speed:
[tex]\[ s = \frac{\text{Total Distance}}{5} \][/tex]
Given that Dan rode more than 175 km in 5 hours, we can express this inequality as:
[tex]\[ \frac{\text{Total Distance}}{5} > \frac{175}{5} \][/tex]
Step 4: Simplifying the Inequality
[tex]\[ s > \frac{175}{5} \][/tex]
[tex]\[ s > 35 \][/tex]
To incorporate the time of 5 hours into the inequality, we multiply both sides by 5:
[tex]\[ 5s > 175 \][/tex]
Step 5: Identifying the Correct Option
From our simplified inequality [tex]\( 5s > 175 \)[/tex], we see that this matches the sentence given in option A.
Therefore, the correct mathematical sentence is:
[tex]\[ \boxed{5s > 175} \][/tex]
Option A is the right answer.
The problem states:
Dan was riding in a bicycle race. After the first five hours of racing, he had ridden more than 175 km. We need to express this situation using a mathematical sentence where [tex]\( s \)[/tex] represents the variable "average speed."
Step 1: Understanding the Concept of Average Speed
The formula for average speed [tex]\( s \)[/tex] is given by:
[tex]\[ s = \frac{\text{Total Distance}}{\text{Total Time}} \][/tex]
Step 2: Applying the Problem's Data
From the problem, we know:
- Total Distance is more than 175 km.
- Total Time is 5 hours.
Step 3: Setting Up the Inequality
Since [tex]\( s \)[/tex] represents the average speed:
[tex]\[ s = \frac{\text{Total Distance}}{5} \][/tex]
Given that Dan rode more than 175 km in 5 hours, we can express this inequality as:
[tex]\[ \frac{\text{Total Distance}}{5} > \frac{175}{5} \][/tex]
Step 4: Simplifying the Inequality
[tex]\[ s > \frac{175}{5} \][/tex]
[tex]\[ s > 35 \][/tex]
To incorporate the time of 5 hours into the inequality, we multiply both sides by 5:
[tex]\[ 5s > 175 \][/tex]
Step 5: Identifying the Correct Option
From our simplified inequality [tex]\( 5s > 175 \)[/tex], we see that this matches the sentence given in option A.
Therefore, the correct mathematical sentence is:
[tex]\[ \boxed{5s > 175} \][/tex]
Option A is the right answer.
