SOLUTION: an airplane travels 900 miles from houston to miami in 6 hors against the wind.on its return trip, with the wind, it takes only 5 hours. find the rate of the airplane with no wind.
Question 264864: an airplane travels 900 miles from houston to miami in 6 hors against the wind.on its return trip, with the wind, it takes only 5 hours. find the rate of the airplane with no wind. find the rate of the wind Found 2 solutions by mananth, ikleyn:Answer by mananth(16949) (Show Source):
You can put this solution on YOUR website! an airplane travels 900 miles from houston to miami in 6 hors against the wind.on its return trip, with the wind, it takes only 5 hours. find the rate of the airplane with no wind. find the rate of the wind
Let the ground speed be x
And the wind speed be y
AGAINST WIND
Distance = 900 miles.
Distance = Rate * time
900= (x-y)*6
WITH WIND
Distance = 900 miles.
Distance = Rate * time
900= (x+y)*5
6x-6y=900
x-y= 150
5x+5y=900
x+y=180
x-y= 150
x+y=180
2x=330
x= 165 mph = ground speed ( With no wind )
y= 15
The ground speed of the plane is 165 mph and wind speed = 15 mph
You can put this solution on YOUR website! .
an airplane travels 900 miles from Houston to Miami in 6 hors against the wind.
on its return trip, with the wind, it takes only 5 hours.
find the rate of the airplane with no wind. find the rate of the wind
~~~~~~~~~~~~~~~~~~~~~~~~
The solution in the post by @mananth is correct: it leads to correct answer.
But the @Mananth' solution is badly organized.
One of the goals of such problems is to teach students to present their solution in perfect
form with straightforward logic.
Therefore I place my solution here.
Let the ground speed be x
And the wind speed be y
AGAINST WIND
Distance = 900 miles.
Rate = Distance/time
x-y = 900/6 = 150 miles per hour.
WITH WIND
Distance = 900 miles.
Rate = Distance/time
x + y = 900/5 = 180 miles per hour.
Thus we have a system of two equations for unknowns x and y
x - y = 150 (1)
x + y = 180 (2)
To find 'x', add the equations. You will get
2x = 150 + 180 = 330 ---> x = 330/2 = 165.
To find 'y', substitute x = 165 in equation (2)
165 + y = 180 ---> y = 180 - 165 = 15.
ANSWER. The rate of the plane with no wind is 165 miles per hour.
The rate of the wind is 15 miles per hour.
