SOLUTION: I am confused on the following problem:
During a 3000 mi flight, a plance encountered a strong tail wind that increased its speed by 100 mi/h. This increase in speed shortened
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Question 312659: I am confused on the following problem:
During a 3000 mi flight, a plance encountered a strong tail wind that increased its speed by 100 mi/h. This increase in speed shortened the flying time by one hour. Find the speed of the plane relative to the ground.
Answer by mananth(16949) (Show Source): You can put this solution on YOUR website!
distance traveled = 3000 miles.
let speed of plane in still air be x mph
speed with tail wind = x+100 mph
..
if it had traveled without any wind it would take 3000 / x hours
with tail wind the time = 3000/x+100.
..
It took 1 hour less.
3000/x - 3000/ x+100 =1
LCM = x(x+100)
3000(x+100) - 3000x = x(x+100)
3000x +300 000 - 3000x = x^2 +100x
x^2+100x-300000=0
x^2 +600x-500x-300000=0
x(x+600)-500(x+600)=0
(x+600)(x-500)=0
x=500 mph in still air
speed with tail wind = 600 mph
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