Question

A plane flies at 450 mph and travels 860 miles with the wind in the same amount of times it travels 740 miles against the wind. solve the equation to find the speed, s, of the wind.

Answer 1

Given that the speed of wind is s,
the total speed traveled by the plane along with the wind will be (450+s) mph.
Similarly, if the plane is against the wind's speed, then it would (450-s) mph.
We must remember that to solve for time, we divide distance by speed.
This means time taken for the plane to travel with the wind at a distance of 860 miles is 860/(450+s).
And time for the plane to travel 740 miles against the wind is 740/(450-s).
Since it took the same amount of time, we can equate both expressions and have

`(860)/(450+s) = (740)/(450-s)`
Working on the equation, we have the following

`860(450-s) = 740(450+s)`

`860(450) - 860s = 740(450) + 740s`

`860(450) - 740(450) = 740s + 860s`

`120(450) = 1600s`

`s = ((120)(450))/(1600)`
From this, we have
`s = 33.75` mph.

Answer 2

The velocity: v = d / t, where d is the distance an t is the amount of time.
Equations are:
450 + s = 860 / t ( with the wind )
450 - s = 740 / t ( against the wind )
s - the speed of the wind
From the 1st equation: s = 860 / t - 450. We can charge it in the 2nd equation:
450 - ( 860 / t - 450 ) = 740 / t
450 - 860 / t + 450 = 740 / t
900 = 860 / t + 740 / t
900 = 1600 / t
t = 1600 : 900
t = 1.77 hours
450 + s = 860 / 1.77
450 + s = 483.75
s = 483.75 - 450
s = 33.75 mph
Answer: The speed of the wind is 33.75 mph.