SOLUTION: a jet plane travelling at a constant speed goes 1200 mi with the wind , then turns around and travels for 1000 mi against the wind . If the speed of the wind is constant 50 mph , a

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: a jet plane travelling at a constant speed goes 1200 mi with the wind , then turns around and travels for 1000 mi against the wind . If the speed of the wind is constant 50 mph , a      Log On


   

Question 109396: a jet plane travelling at a constant speed goes 1200 mi with the wind , then turns around and travels for 1000 mi against the wind . If the speed of the wind is constant 50 mph , and the total flight took 4 hrs , find the speed of the plane.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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jet plane traveling at a constant speed goes 1200 mi with the wind , then turns around and travels for 1000 mi against the wind . If the speed of the wind is constant 50 mph , and the total flight took 4 hrs , find the speed of the plane.
:
Let s = speed of the plane
then
(s+50) = speed with the wind
and
(s-50) = speed against the wind
:
Write a time equation: Time = dist/speed
:
Time with + time against = 4 hr
1200%2F%28%28s%2B50%29%29 + 1000%2F%28%28s-50%29%29 = 4
:
Multiply equation by (s+50)(s-50) to eliminate the denominators:
(s+50)(s-50)*1200%2F%28%28s%2B50%29%29 + (s+50)(s-50)*1000%2F%28%28s-50%29%29 = 4(s+50)(s-50)
:
Cancel out the denominators and you have;
1200(s-50) + 1000(s+50) = 4(s^2 - 2500)
:
1200s - 60000 + 1000s + 50000 = 4s^2 - 10000
:
2200s - 10000 = 4s^2 - 10000
:
Arrange as quadratic equation on the left:
4s^2 - 2200s - 10000 + 10000 = 0
:
4s^2 - 2200s = 0
:
Factor this:
4s(s - 550) = 0
:
Solution:
4s = 0
s = 0
and
s = +550 mph is our solution; (speed of the plane in still air)
:
:
Check our solution, find the time total:
speed with the wind: 600 mph
speed against the wind: 500 mph
1200/600 + 1000/500
2 + 2 = 4hrs