A bomber takes off and flies at 500kph. A fighter, setting out 2 1/2 hrs later flies at 750kph. How long will it take for the fighter to catch the bomber, and how far will the bomber have travelled at this time?

To solve this problem, we can use the concept of relative speed. Relative speed is the difference in speeds between two moving objects. In this case, the relative speed between the bomber and the fighter is 750 kph - 500 kph = 250 kph.

Let's calculate the time it takes for the fighter to catch the bomber:

Since the fighter sets out 2 1/2 hours later than the bomber, we need to account for this time difference. We'll subtract 2 1/2 hours from the time it takes for the fighter to catch up.

Let's call the time it takes for the fighter to catch up "t" hours.

Distance covered by the fighter = Relative speed × time
Distance covered by the bomber = Bomber's speed × time

As the fighter catches up to the bomber, the distance covered by both will be equal. So, we can set up the equation:

250t = 500t

Now, we can solve for "t":

250t = 500t
250t - 500t = 0
-250t = 0
t = 0

The time it takes for the fighter to catch the bomber is 0 hours. This means the fighter catches the bomber instantly, assuming the initial positions of the two planes were the same.

To calculate the distance the bomber traveled at this time, we can use the formula:

Distance = Speed × Time

The time taken by the bomber is "t", which we just found to be 0 hours. So, the distance traveled by the bomber is 500kph × 0 hours = 0 km.

Therefore, at the time the fighter catches the bomber, the bomber will have traveled 0 km.