Add more problems and solutions to this please
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.
Problem: A car travels 320 miles in 4 hours. If the car maintains the same speed, how long will it take to travel 480 miles?
Solution:
Once again, using proportionality, let "t" represent the time it will take to travel 480 miles.
We know that the car 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:
320 miles / 4 hours = 480 miles / t hours
To solve for t, we can cross multiply:
320 * t = 480 * 4
320t = 1920
To isolate t, we divide both sides of the equation by 320:
320t / 320 = 1920 / 320
t = 6
Therefore, it will take 6 hours for the car to travel 480 miles if it maintains the same speed.
Problem: A plane flies 900 kilometers in 2 hours. If the plane maintains the same speed, how far will it fly in 5 hours?
Solution:
Using proportionality, let "d" represent the distance the plane will fly in 5 hours.
We know that the plane 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:
900 kilometers / 2 hours = d kilometers / 5 hours
To solve for d, we can cross multiply:
900 * 5 = 2 * d
4500 = 2d
To isolate d, we divide both sides of the equation by 2:
4500 / 2 = d
2250 = d
Therefore, the plane will fly 2250 kilometers in 5 hours if it maintains the same speed.