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?
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To find the distance at which bike A and bike B will be equal distances from the starting point, we need to set up an equation.
Let x be the distance in miles from the starting point that both bikes have traveled.
For bike A, the distance from the starting point is 50 + x miles.
For bike B, the distance from the starting point is 100 + x miles.
Since the speed is equal to the distance divided by the time, the time traveled for both bikes will be the same.
The time traveled for bike A is given by t = (50 + x) / 30.
The time traveled for bike B is given by t = (100 + x) / 25.
Since the time traveled is the same for both bikes, we can set these two equations equal to each other:
(50 + x) / 30 = (100 + x) / 25.
To solve for x, we can cross multiply:
25(50 + x) = 30(100 + x).
1250 + 25x = 3000 + 30x.
Subtracting 25x and 3000 from both sides, we have:
-1750 = 5x.
Dividing both sides by 5, we find:
-350 = x.
Since distance cannot be negative in this context, x = 350 miles.
Therefore, bike A and bike B will be the same distance from the starting point after traveling 350 miles.
Why did the bikes have to be in a race? Couldn't they just peacefully coexist at different distances from the starting point? Poor Bike A and Bike B, always going head to head. But I digress.
To solve this question, let's assume they travel for 'x' hours until they are the same distance from the starting point. Thus, Bike A will travel 30x miles and Bike B will travel 25x miles.
Now, we need to find when the distances of both bikes are equal. So, we can set up an equation:
50 + 30x = 100 + 25x
If we simplify this equation, we get:
5x = 50
Dividing both sides by 5, we find:
x = 10
Therefore, after 10 hours, Bike A and Bike B will be the same distance from the starting point. But don't worry, they can still be friends even if they're not neck and neck in a race!
To find out after how many miles bike A and bike B will be the same distance from the starting point, we can set up an equation.
Let's assume it takes x hours for both bikes to be the same distance from the starting point.
For Bike A:
Distance = Speed * Time
So, the distance traveled by Bike A after x hours is 30x miles.
For Bike B:
Distance = Speed * Time
So, the distance traveled by Bike B after x hours is 25x miles.
To find when the distances are equal, we set up the equation:
30x = 25x.
To solve for x, we subtract 25x from both sides of the equation:
30x - 25x = 0.
Simplifying, we have:
5x = 0.
Dividing both sides of the equation by 5, we get:
x = 0.
Therefore, after 0 hours (or at the starting point), Bike A and Bike B will be at the same distance from the starting point.
To find out at which point bike A and bike B will be at the same distance from the starting point, you need to determine the time it takes for each bike to reach that point.
Let's assume that after a certain time, t, bike A and bike B will be at the same distance from the starting point.
For bike A:
Distance = Speed * Time
Distance = 30 mph * t
For bike B:
Distance = Speed * Time
Distance = 25 mph * t
Now, equate the distances of bike A and bike B to find the value of t:
30t = 25t
Simplifying the equation, we find:
5t = 0
Since 5t equals 0, it means that both bikes will always be at the same distance from the starting point.
Therefore, the answer is that bike A and bike B will be at the same distance from the starting point regardless of the number of miles traveled.