Can you add more problems and solutions to this?
Problem: A car travels 300 miles in 5 hours. If the car maintains the same speed, how far will it travel in 8 hours?
Solution:
We can set up a proportion to solve this problem. Let's use "x" to represent the distance the car will travel in 8 hours.
We know that the car maintains the same speed throughout the journey. Therefore, we can say that the distance traveled is directly proportional to the time taken.
The proportion can be set up as:
300 miles / 5 hours = x miles / 8 hours
To solve for x, we can cross multiply:
300 * 8 = 5 * x
2400 = 5x
To isolate x, we divide both sides of the equation by 5:
2400 / 5 = x
480 = x
Therefore, the car will travel 480 miles in 8 hours if it maintains the same speed.
Here are some additional problems and solutions:
Problem: A train travels 400 kilometers in 6 hours. If the train maintains the same speed, how long will it take to travel 600 kilometers?
Solution:
Using the same concept of proportionality, let's use "t" to represent the time it will take to travel 600 kilometers.
We know that the train maintains the same speed throughout the journey. Therefore, we can say that the time taken is directly proportional to the distance traveled.
The proportion can be set up as:
400 kilometers / 6 hours = 600 kilometers / t hours
To solve for t, we can cross multiply:
400 * t = 600 * 6
400t = 3600
To isolate t, we divide both sides of the equation by 400:
400t / 400 = 3600 / 400
t = 9
Therefore, it will take 9 hours for the train to travel 600 kilometers if it maintains the same speed.
Problem: A cyclist bike rides 60 miles in 3 hours. If the cyclist maintains the same speed, how far will they travel in 7 hours?
Solution:
Again, using proportionality, let's use "d" to represent the distance the cyclist will travel in 7 hours.
We know that the cyclist maintains the same speed throughout the journey. Therefore, we can say that the distance traveled is directly proportional to the time taken.
The proportion can be set up as:
60 miles / 3 hours = d miles / 7 hours
To solve for d, we can cross multiply:
60 * 7 = 3 * d
420 = 3d
To isolate d, we divide both sides of the equation by 3:
420 / 3 = d
140 = d
Therefore, the cyclist will travel 140 miles in 7 hours if they maintain the same speed.