Question

The sound of a gunfire travelled 350 m a second with the wind and 320m a second against the wind . Find velocity of the sound and the rate at which the wind was blowing.

Answer 1

Step 1 : Assigning the variables

To represent the unknown quantities by two variables

Let the velocity of the sound of a gunfire x m and the velocity of the wind blowing be y m/s

Step 2 :Framing Equation

According to the question

The velocity of a gunfire travelled with the wind is x + y = 350 ----- 1

The velocity of a gunfire travelled against the wind is x - y = 320 ----- 2

Step 3 : Elimination method

Solve the equation 1 & 2 using elimination method

Adding equation 1 & 2 we get

$$\begin{gathered} 2x=670 \\ x=\frac{670}{2}=335 \end{gathered}$$

Step 4 : Substituting values

Substitute the value of x = 335 in equation

1 we get,

$$\begin{gathered} 335+y=350 \\ y=350-335=15 \end{gathered}$$

Hence the velocity of the sound of a gunfire is 335 m/s and the velocity of the wind blowing is 15m/s .