A plane flies 720 miles against a 30miles per hour headwind and then returns to the same point with the wind. If the entire trip takes 10 hours, what is the plane's speed in still air?
2007-01-03 06:37:39 · 4 answers · asked by Ebbie W 1 in Science & Mathematics ➔ Mathematics
Firstlenn had the right idea, but I checked her answers in the equation and I got 11 hours instead of 10. So i'm going to do it too.
Her basic equation is correct. t = d/r, so for the first half of the trip, the plane took 720/(x - 30) hours and for the second half, the plane took 720/(x + 30) hours, and the sum of the two makes 10 hours:
720/(x - 30) + 720/(x + 30) = 10
Multiply through by (x - 30)(x + 30):
720(x + 30) + 720(x - 30) = 10(x - 30)(x + 30)
720x + 210 + 720x - 210 = 10(x² - 900)
1440x = 10x² - 9000
0 = 10x² - 1440x - 9000
0 = x² - 144x - 900
Ah, so I think she missed a sign...
Factoring:
0 = (x - 150)(x + 6)
Therefore x = 150 (and you can throw out the -6, because I can't imagine a plane going -6 miles per hour).
So the plane's speed in still air is 150 miles per hour.
Checking:
720/(150 - 30) + 720/(150 + 30)
= 720/120 + 720/180
= 6 + 4
= 10...check!
2007-01-03 07:14:52 · answer #1 · answered by Jim Burnell 6 · 0⤊ 0⤋
two answer this question you need to form distance over speed is equal to time. This gives you
720/(x-30) + 720/(x+30) = 10
do some algebra and retrieve the equation
x^2-144x+900=0
which gives 137.45 and 6.547
you can easily see that the second answer makes no sense as the plane has travelled 1440 miles in 10 hours.
2007-01-03 06:48:43 · answer #2 · answered by firstlennsman 1 · 0⤊ 0⤋
42
2007-01-03 06:39:34 · answer #3 · answered by novae2 3 · 0⤊ 1⤋
Do your own homework.
2007-01-03 06:39:23 · answer #4 · answered by ? 6 · 1⤊ 1⤋