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? (1 point)
To determine the time it takes for each bike to travel the same distance from the starting point, we can set up the equation:
distance = speed × time
For bike A, we have:
50 miles = 30 miles/hour × time
Simplifying the equation for bike A, we get:
time = 50 miles / 30 miles/hour
time = 5/3 hours
Now, let's set up the equation for bike B:
distance = speed × time
distance = 25 miles/hour × time
Since both bikes will travel the same distance from the starting point, we can set their distances equal to each other:
30t = 25t
Next, we solve for t:
30t - 25t = 0
5t = 0
t = 0
Therefore, both bike A and bike B will be the same distance from the starting point after 0 hours.
To find the point at which both bike A and bike B are the same distance from the starting point, we can set up an equation based on their distances and speeds.
Let's assume that after t hours, both bikes will be the same distance from the starting point.
The distance traveled by bike A after t hours can be calculated using the formula: Distance = Speed × Time. Therefore, the distance traveled by bike A after t hours is 30t.
The distance traveled by bike B after t hours can also be calculated using the formula: Distance = Speed × Time. Therefore, the distance traveled by bike B after t hours is 25t.
We want to find the value of t at which both distances are equal. So, we can set up the equation:
30t = 25t
Now, we can solve this equation to find the value of t:
30t - 25t = 0 (subtract 25t from both sides)
5t = 0 (combine like terms)
t = 0 (divide both sides by 5)
Therefore, bike A and bike B will be the same distance from the starting point after 0 hours, which means they are already at the same distance from the starting point.