Question

A plane can travel 640 miles against the wind in the same time it can travel 800 miles with the wind. If the plane can fly 180 mph in calm air, what is the speed of the wind? 10 mph 15 mph 20 mph

Answer 1

Answer:

20 mph

Step-by-step explanation:

Let the speed of the wind be x

Speed of the plane is 180 mph

When plane flew with wind , Speed = (180+x)

When plane flew against the wind , Speed=(180-x)

Since we are given that A plane can travel 640 miles against the wind .

$Time = \frac{Distance }{Speed}$

$\Rightarrow Time = \frac{640}{180-x}$  --A

It can travel 800 miles with the wind.

$\Rightarrow Time = \frac{800}{180+x}$ --B

Now we are given that the plane travels with the same time in both cases.

So, equation A = equation B

$\frac{640}{180-x}= \frac{800}{180+x}$

$640(180+x)= 800(180-x)$

$115200+640x= 144000-800x$

$640x+800x= 144000-115200$

$1440x= 28800$

$x= \frac{28800}{1440}$

$x= 20$

Hence the speed of the wind is 20 mph

Answer 2

Here is how to solve it:
Distance1 ÷ (plane velocity + wind velocity) = Distance2 ÷ (plane velocity - wind velocity)800 / (180 + wv) = 640 / (180 - wv)

115,200 +640 wv = 144,000 - 800 wv

1,440 wv = 28,800

wind velocity = 20 mph

Source:
http://www.1728.org/veloccal.htm