SOLUTION: Two seconds after firing a rifle at a target, the shooter hears the impact of the bullet. Sound travels at 1100 feet per second and the bullet at 1865 feet per second. Determine th

Question 350851: Two seconds after firing a rifle at a target, the shooter hears the impact of the bullet. Sound travels at 1100 feet per second and the bullet at 1865 feet per second. Determine the distance to the target.
How do you set up that equation?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sound travels at 1100 feet per second.

bullet travels at 1865 feet per second.

person fires bullet and hears the sound of the bullet hitting the target 2 seconds later.

we want to find the distance to the target.

since rate * time = distance, we know that:

1865 * x = d

where x is the time it takes for the bullet to get to the target and d is the distance to the target.

1100 * y = d where y is the time it takes for the sound of the bullet hitting the target to get back to the shooter and d is the distance from the target to the shooter.

since the distance to the target and the distance back from the target are the same, then we can set these equations equal to each other to get:

1865*x = 1100*y = d

we also know that the total time is equal to 2 seconds.

this means that x + y must equal 2.

we can solve for x or y from this equation.

we'll solve for y.

we get y = (2-x)

we take the equation of 1865*x = 1100*y and substitute for y to get:

1865*x = 1100*(2-x)

simplify this to get:

1865*x = 2200 - 1100*x

add 1100*x to both sides of this equation to get:

2965*x = 2200

divide both sides of this equation by 2965 to get:

x = 2200/2965 = .741989882 seconds

since x + y = 2, this makes y = 1.258010118

it takes the bullet .741989882 seconds to reach the target and it takes the sound of the bullet hitting the target 1.258010118 seconds to get back to the shooter.

x + y must equal 2 which we get by adding .741989882 + 1.258010118 = 2

the distance to the target and the distance back from the target must be the same.

1865 * .741989882 = 1383.81113 feet.

1100 * 1.258010118 = 1383.81113 feet.

distances are the same so the numbers must be good.

The distance to the target is 1183.81113 feet.

the shooter fires the bullet.
it takes .741989882 seconds for the bullet to reach the target.
it takes 1.258010118 seconds for the sound of the bullet hitting the target to get back to the shooter.
the shooter hears the sound 2 seconds after the shooter fires the bullet.

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