Question

Flying against the wind, a jet travels 2920 miles in 4 hours. Flying with the wind, the same jet travels 7140 miles in 6 hours. What is the rate of the jet in still air and what is the rate of the wind

Answer 1

Answer:

Velocity in still air is = 960 miles per hour  

Velocity of wind  = 230 miles per hour.

Step-by-step explanation:

The velocity when flying against the wind = 2920 / 4 = 730 miles per hour.

The velocity when flying with the wind = 7140 / 6 = 1190

Let the rate of jet in still Air = x

Let the rate of jet in wind = y

Therefore, velocity against wind = x-y and wind = x + y

x - y = 730

x + y = 1190

Add both equation, 2x = 1920

x = 960

Now find the value of “y” = 1190 – 960 = 230

Thus, velocity in still air is = 960 miles per hour  

Velocity of wind  = 230 miles per hour.

Answer 2

Answer:

Rate of jet in still air = 960 miles/ hr

Rate of the wind = 230 miles/ hr

Step-by-step explanation:

Let the speed of jet in still air = $u$ miles/hr

Let the speed of air = $v$ miles/hr

So, against the wind, the resultant speed = $(u-v)$ miles/hr

And, with the wind, the resultant speed = $(u+v)$ miles/hr

Distance traveled against the wind = 2920 miles

Time taken against the wind = 4 hrs

Formula for distance is:

$\bold{Distance =Speed \times Time}$

$2920 = (u-v)\times 4\\\Rightarrow u-v=\dfrac{2920}{4}\\\Rightarrow u-v=730\ miles/hr...... (1)$

Distance traveled with the wind = 7140 miles

Time taken against the wind = 6 hrs

$\bold{Distance =Speed \times Time}$

$7140 = (u+v)\times 6\\\Rightarrow u+v=\dfrac{7140}{6}\\\Rightarrow u+v= 1190 \ miles/hr...... (2)$

Adding (1) and (2):

$2u = 1920\\\Rightarrow \bold{u = 960 miles/hr}$

Putting $u$ in (1):

$960 -v = 730 \\\Rightarrow \bold{v=230\ miles/hr}$

Therefore, the answer is:

Rate of jet in still air = 960 miles/ hr

Rate of the wind = 230 miles/ hr