Answer :
To solve this problem, we need to find the correct mathematical translation of the given scenario involving Dan's bicycle race. We're told that after the first five hours of racing, Dan had ridden more than 175 km. We want to express this as a mathematical inequality where [tex]\( s \)[/tex] is Dan's average speed in kilometers per hour.
Here's how we can approach the problem:
1. Understand the Situation:
- Dan has been riding for 5 hours.
- He has covered more than 175 km in that time.
2. Represent the Situation Mathematically:
- The formula to calculate the distance is: [tex]\(\text{distance} = \text{speed} \times \text{time}\)[/tex].
- In this case, the distance Dan traveled after 5 hours is more than 175 km.
- Let the average speed be [tex]\( s \)[/tex]. The equation for the distance after 5 hours would then be [tex]\( 5s \)[/tex].
3. Set Up the Inequality:
- Since Dan's distance is more than 175 km, we can write this as:
[tex]\[
5s > 175
\][/tex]
4. Match the Inequality to the Given Options:
- Option B is [tex]\( 5s > 175 \)[/tex], which matches our inequality perfectly.
Therefore, the correct translation of the situation is option B: [tex]\( 5s > 175 \)[/tex].
This tells us that Dan's average speed was more than [tex]\( \frac{175}{5} \)[/tex] km/h, showing that his speed was consistently greater to cover more than 175 km in 5 hours. Based on the information, option B accurately represents the situation.
Here's how we can approach the problem:
1. Understand the Situation:
- Dan has been riding for 5 hours.
- He has covered more than 175 km in that time.
2. Represent the Situation Mathematically:
- The formula to calculate the distance is: [tex]\(\text{distance} = \text{speed} \times \text{time}\)[/tex].
- In this case, the distance Dan traveled after 5 hours is more than 175 km.
- Let the average speed be [tex]\( s \)[/tex]. The equation for the distance after 5 hours would then be [tex]\( 5s \)[/tex].
3. Set Up the Inequality:
- Since Dan's distance is more than 175 km, we can write this as:
[tex]\[
5s > 175
\][/tex]
4. Match the Inequality to the Given Options:
- Option B is [tex]\( 5s > 175 \)[/tex], which matches our inequality perfectly.
Therefore, the correct translation of the situation is option B: [tex]\( 5s > 175 \)[/tex].
This tells us that Dan's average speed was more than [tex]\( \frac{175}{5} \)[/tex] km/h, showing that his speed was consistently greater to cover more than 175 km in 5 hours. Based on the information, option B accurately represents the situation.
