Type The Correct Answer In Each Box. Use Numbers Instead Of Words.A Cyclist Rides 8 Kilometers In 0.4 Hours.Complete The Sentence To Determine The Unit Rate And How Far The Cyclist Can Ride In 2 Hours At The Same Speed.The Cyclist Has A Unit Rate Of
Understanding Unit Rates
A unit rate is a ratio of two quantities, where the second quantity is one unit. In the context of the given problem, the unit rate represents the distance a cyclist can travel in one hour at a constant speed. To determine the unit rate, we need to divide the total distance traveled by the total time taken.
Calculating the Unit Rate
Given that the cyclist rides 8 kilometers in 0.4 hours, we can calculate the unit rate as follows:
- Distance = 8 kilometers
- Time = 0.4 hours
To find the unit rate, we divide the distance by the time:
Unit Rate = Distance ÷ Time = 8 km ÷ 0.4 hours = 20 km/h
Interpreting the Unit Rate
The unit rate of 20 km/h indicates that the cyclist can travel 20 kilometers in one hour at the same speed. This means that if the cyclist maintains the same speed, they can cover a certain distance in a given time.
Determining the Distance Traveled in 2 Hours
Now that we have the unit rate, we can use it to determine the distance the cyclist can ride in 2 hours at the same speed. We can set up a proportion to relate the unit rate to the given time:
- Unit Rate = 20 km/h
- Time = 2 hours
We can set up the proportion as follows:
20 km/h = x km / 2 hours
To solve for x, we can cross-multiply:
20 km/h × 2 hours = x km 40 km = x km
Conclusion
In conclusion, the cyclist has a unit rate of 20 km/h, indicating that they can travel 20 kilometers in one hour at the same speed. Using this unit rate, we can determine that the cyclist can ride 40 kilometers in 2 hours at the same speed.
Key Takeaways
- A unit rate is a ratio of two quantities, where the second quantity is one unit.
- To determine the unit rate, we divide the distance by the time.
- The unit rate can be used to determine the distance traveled in a given time at the same speed.
Practice Problems
- A car travels 120 miles in 2 hours. What is the unit rate of the car?
- A person walks 3 kilometers in 0.5 hours. What is the unit rate of the person?
- A bike travels 15 kilometers in 1.5 hours. What is the unit rate of the bike?
Answer Key
- 60 miles/hour
- 6 kilometers/hour
- 10 kilometers/hour
Frequently Asked Questions (FAQs) =====================================
Q: What is a unit rate?
A: A unit rate is a ratio of two quantities, where the second quantity is one unit. It represents the rate at which a quantity changes with respect to a unit change in another quantity.
Q: How do I calculate the unit rate?
A: To calculate the unit rate, you need to divide the distance by the time. For example, if a cyclist rides 8 kilometers in 0.4 hours, the unit rate would be 8 km ÷ 0.4 hours = 20 km/h.
Q: What is the difference between a unit rate and a rate?
A: A rate is a ratio of two quantities, whereas a unit rate is a ratio of two quantities where the second quantity is one unit. For example, a rate of 20 km/h is different from a unit rate of 20 km/h, as the latter represents the distance traveled in one hour.
Q: Can I use the unit rate to determine the distance traveled in a given time?
A: Yes, you can use the unit rate to determine the distance traveled in a given time. For example, if the unit rate is 20 km/h and the time is 2 hours, the distance traveled would be 20 km/h × 2 hours = 40 km.
Q: What if the time is not given in hours? How do I calculate the unit rate?
A: If the time is not given in hours, you can convert it to hours by dividing the time by the number of hours in the given time unit. For example, if the time is given in minutes, you can convert it to hours by dividing the time by 60.
Q: Can I use the unit rate to compare the rates of different objects?
A: Yes, you can use the unit rate to compare the rates of different objects. For example, if the unit rate of a car is 60 miles/hour and the unit rate of a bike is 10 miles/hour, you can compare the rates of the two objects.
Q: What if the unit rate is not a whole number? How do I interpret it?
A: If the unit rate is not a whole number, you can interpret it as a decimal or a fraction. For example, if the unit rate is 20.5 km/h, you can interpret it as 20.5 kilometers per hour.
Q: Can I use the unit rate to determine the time taken to travel a given distance?
A: Yes, you can use the unit rate to determine the time taken to travel a given distance. For example, if the unit rate is 20 km/h and the distance is 40 km, you can determine the time taken by dividing the distance by the unit rate: 40 km ÷ 20 km/h = 2 hours.
Q: What if I have multiple unit rates? How do I compare them?
A: If you have multiple unit rates, you can compare them by dividing the unit rates. For example, if the unit rate of a car is 60 miles/hour and the unit rate of a bike is 10 miles/hour, you can compare the rates by dividing the unit rates: 60 miles/hour ÷ 10 miles/hour = 6.
Q: Can I use the unit rate to determine the rate of change of a quantity?
A: Yes, you can use the unit rate to determine the rate of change of a quantity. For example, if the unit rate is 20 km/h, you can determine the rate of change of the distance traveled by multiplying the unit rate by the time: 20 km/h × 2 hours = 40 km.
Q: What if I have a negative unit rate? How do I interpret it?
A: If you have a negative unit rate, you can interpret it as a rate of decrease. For example, if the unit rate is -20 km/h, you can interpret it as a rate of decrease of 20 kilometers per hour.
Q: Can I use the unit rate to determine the rate of change of a quantity over a given time period?
A: Yes, you can use the unit rate to determine the rate of change of a quantity over a given time period. For example, if the unit rate is 20 km/h and the time period is 2 hours, you can determine the rate of change of the distance traveled by multiplying the unit rate by the time period: 20 km/h × 2 hours = 40 km.