Solve the problem.A cyclist bikes at a constant speed for 25 miles. He then returns home at the same speed but takes a different route. His return trip takes one hour longer and is 30 miles. Find his speed.

since time=distance/speed,

25/x + 1 = 30/x
x = 5

some slow rider!

To solve this problem, let's start by assigning variables to the unknowns. Let's call the cyclist's speed "s" (in miles per hour).

We know that the cyclist bikes at a constant speed for 25 miles. Using the formula: speed = distance/time, we can write the equation:

s = 25 miles / t1

Where t1 represents the time it takes to cover the 25 miles.

Next, we are told that the cyclist returns home at the same speed but takes a different route, which is 30 miles. This time, the return trip takes one hour longer. So, the equation for the return trip would be:

s = 30 miles / (t1 + 1 hour)

We can now set up an equation by equating these two expressions for speed:

25 miles / t1 = 30 miles / (t1 + 1 hour)

To solve for "s", we need to isolate "t1" in this equation and then substitute the value back into one of the original equations.

First, let's simplify the equation by cross-multiplying:

25(t1 + 1 hour) = 30t1

25t1 + 25 hours = 30t1

Next, let's isolate "t1" on one side of the equation:

25 hours = 30t1 - 25t1

25 hours = 5t1

Divide both sides of the equation by 5:

5 hours = t1

Now that we have the value of "t1", we can substitute it back into one of the original equations to solve for the speed "s". Let's use the first equation:

s = 25 miles / t1

s = 25 miles / 5 hours

s = 5 miles per hour

Therefore, the cyclist's speed is 5 miles per hour.