Question 828684: A plane flew 720 miles with a steady 30 mph tailwind. The pilot then returned to the starting point, flying against the wind. If the round trip flight took 10 hours, what was the plane's airspeed?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
s = d/t
t = d/s
---
x = airplane speed
y = wind speed
---
ta = 720/(x + y)
tb = 720/(x - y)
ta + tb = 10
---
720/(x + y) + 720/(x - y) = 10
720(x - y)/(x + y)(x - y) + 720(x + y)/(x + y)(x - y) = 10
720(x - y) + 720(x + y) = 10(x + y)(x - y)
720x - 720y + 720x + 720y = 10(xx - xy + xy - yy)
1440x = 10(xx - yy)
10xx - 1440x - 10yy = 0
10xx - 1440x - 10*30*30 = 0
10xx - 1440x - 9000 = 0
---
the above quadratic equation is in standard form, with a=10, b=-1440, and c=-9000
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
10 -1440 -9000
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
---
the quadratic has two real roots at:
---
x = 150
x = -6
---
the negative root doesn't fit the problem statement, so use the positive root:
---
answer:
x = airplane speed = 150 mph
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
|
|
|
