# How do I measure distance in this problem?

I am posting here again after a long time. I have this distance measuring problem that I have been trying to solve. Please help me out here. TIA.

***A bullet covers distance of 1540 feet per second. Given the measurement, a person fired a shot and heard the sound of hitting the destination point after 3 seconds of firing. Speed of sound is 1100 feet per second.

What is the distance of destination point here?***

Regards Imran

• You have to visualize what happens: First, the bullet travels to the destination (you have to calculate how long this takes) and then the sound of the impact travels back to the shooter (again, you have to calculate how long this takes). The total time is known, and you have to solve for the distance. So you will have the sum of two terms, and the sum is equal to 3 seconds. Commented Feb 25, 2019 at 8:10
• I changed the tag to correctly reflect the category to which the problem belongs. (The tag 'measure-theory' is related to abstract theory of integration.) Hope this helps. @SujitBhattacharyya, Sorry, I edited the tag and accidentally rendered your comment no longer relevant. Hope you don't mind this. Commented Feb 25, 2019 at 8:13
• Sorry about tags. I am new here and not so familiar with tags. Commented Feb 25, 2019 at 8:36
• @Imran you are welcome. I removed my comment. Commented Feb 25, 2019 at 16:12

Let $$d$$ denote such distance. Then the total time for the bullet to reach the destination and for the person to hear the sound of hitting is simply $$\frac{d}{1540}+\frac{d}{1100}.$$ By condition, this should equal $$3$$. The answer will follow after your solving the equation about $$d$$: $$\frac{d}{1540}+\frac{d}{1100}=3.$$