Question

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?

Help

Answer 1

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.