Question

An airplane travels 600 miles against the wind in 4 hours, and makes the return trip with then same wind in 2 hours. Find the speed of the wind.

Answer 1

Answer:

The speed of wind is 75 miles / hour

Step-by-step explanation:

Let's assume

speed of airplane is x miles /hour

speed of wind is y miles /hour

Against wind:

An airplane travels 600 miles against the wind in 4 hours

against wind means resultant speed will be less

so, speed =x-y

total distance traveled in 4 hour is

$=4(x-y)$

and this has to be equal to 600

$600=4(x-y)$

Divide both sides by 4

and we get

$x-y=150$

With wind:

makes the return trip with then same wind in 2 hours

with wind means resultant speed will be more

so, speed =x+y

total distance traveled in 2 hour is

$=2(x+y)$

and this has to be equal to 600

$600=2(x+y)$

Divide both sides by 2

and we get

$x+y=300$

So, we get system of equations

$x-y=150$

$x+y=300$

now, we can solve it by adding both equations

$x-y+x+y=150+300$

$2x=450$

now, we can solve for x

$x=225$

now, we can  find y by plugging x into any one equation

$225+y=300$

$y=75$

So,

The speed of wind is 75 miles / hour