Suppose you fire a rifle bullet at1600 m/s in a shooting gallery and hear the gong on the target ring 0.723 seconds later. taking the speed of sound to be 326 m/s and assuming the bullet travels straight downrange at a constant speed, how many far away is the target?

The total time would be the sum of time for the bullet to reach the gong and the time it takes the sound to reach you.

So we have:

0.723 s = time for bullet to reach gong + time for sound to reach you

Let us say that D is the distance, then time for bullet to reach gong is D/1600

While the time for sound to reach you is D/326

therefore we get

0.723 = D/1600 + D/326

D = 0.723 / (1/1600 + 1/326)

D = 195.8 m