In a bike race, bike A is 50 miles from the starting point and travels 30 miles per hour. Bike B is 100 miles from the starting point and travels 25 miles per hour. After how many miles will bike A and bike B be the same distance from the starting point?
Let x be the distance from the starting point at which bike A and bike B are the same distance from the starting point.
The time it takes for bike A to travel this distance is x / 30.
The time it takes for bike B to travel this distance is (100 - x) / 25.
Therefore, x / 30 = (100 - x) / 25.
Multiplying both sides by 30*25, we get 25x = 30 * (100 - x).
Expanding the right side, we get 25x = 3000 - 30x.
Combining like terms, we get 55x = 3000.
Dividing both sides by 55, we get x = 3000 / 55 = <<3000/55=54.55>>54.55.
Therefore, bike A and bike B will be the same distance from the starting point after 54.55 miles.
To find the point at which Bike A and Bike B are the same distance from the starting point, we need to determine when they have both traveled the same distance.
Let's assume that after traveling x miles, Bike A and Bike B will be at the same distance from the starting point.
For Bike A:
Distance covered by Bike A = 30 miles/hour * time traveled
Distance covered by Bike A = 30 * x
For Bike B:
Distance covered by Bike B = 25 miles/hour * time traveled
Distance covered by Bike B = 25 * x
Since we want to find the distance at which Bike A and Bike B are the same, we can set up the following equation:
30x = 25x + 50
Simplifying the equation:
30x - 25x = 50
5x = 50
x = 10
So, after 10 miles, Bike A and Bike B will both be the same distance from the starting point.