Question

Use the three steps to solve the problem. With a certain tail wind a jet aircraft arrives at its destination, 1,890 miles away, in 3 hours. Flying against the same wind, the plane makes the return trip in 3 3/8 hours. Find the wind speed and the plane's airspeed. {wind speed is ? a0 mph, airspeed is ?
a1 mph}

Answer 1

Answer: The wind's speed is  35 miles/hour

The aircraft's speed is 595 miles/hour.

Step-by-step explanation:

Given: Distance =1890 miles

Let speed of aircraft be 'u' and the speed of the wind be 'v'.

With a certain tail wind a jet aircraft arrives at its destination, 1,890 miles away, in 3 hours.

∴ the relative speed = u+v=$\frac{distance}{time}$

⇒ (u+v)=1890/3=630................(1)

Flying against the same wind, the plane makes the return trip in 3 3/8 (27/8)hours.

⇒ ∴ the relative speed = u-v=$\frac{distance}{time}$

⇒u-v=$\frac{1890}{\frac{27}{8}}=\frac{1890\times3}{27}=560$.................(2)

addind (1) and (2),we get

2u=630+560=1190

⇒u=1190/2=595 miles/hour

Substitute u=595 in (1),we get

⇒595+v=630

⇒v=630-595=35 miles/hour.

Therefore ,the wind's speed is v = 35miles/hour

the aircraft's speed is u = 595 miles/hour.

Answer 2

To answer this item, we let x be the speed of the jet plane in still air and y be the speed of the wind. It is known that distance traveled by an object is the product of its speed and the time. With this concept, the linear equation that would allow us to solve the problem is,
  
       (x + y)(3) = 1890
       (x - y)(3 3/8) = 1890

The values of x and y from the equation are 595 and 35.

Answer: speed of the wind = 35 mi/h
              speed of aircraft = 595 mi/h