Two bicycle riders, Jeff and Nancy, are 25 miles apart, riding toward each other at speeds of 15 mph and 10 mph, respectively. A fly starts from Jeff and flies toward Nancy and then back to Jeff again and so on. The fly continues flying back and forth at a constant rate of 40 mph, until the bicycle riders "collide" and crush the fly. How far has the fly traveled?

it takes the riders one hour to "collide"

the fly is flying at 40 miles per hour

To find out how far the fly has traveled, we can calculate the time it takes for the bicycle riders to collide.

Let's first find the total speed at which the bicycle riders are approaching each other:
Total speed = Jeff's speed + Nancy's speed
Total speed = 15 mph + 10 mph
Total speed = 25 mph

Now, we can use the formula: Distance = Speed × Time
Since the fly is covering the same distance as the riders, we can equate their distances.

Let's assume the time taken for the riders to collide is "t" hours.

Distance covered by Jeff = Jeff's speed × t = 15t miles
Distance covered by Nancy = Nancy's speed × t = 10t miles

Since they are 25 miles apart, the total distance covered by both riders combined is 25 miles. So we have the equation:

Distance covered by Jeff + Distance covered by Nancy = Total distance
15t + 10t = 25
25t = 25
t = 1 hour

Now that we know the riders will collide after 1 hour, we can calculate how far the fly has traveled by multiplying its speed by the time.

Distance traveled by the fly = Fly's speed × Time taken by the riders to collide
Distance traveled by the fly = 40 mph × 1 hour
Distance traveled by the fly = 40 miles

Therefore, the fly has traveled 40 miles.