The speed of a airplane in still air is 235 Km/h.the plane travels 498 Km/h against the wind, and 1378 Km with the wind, in a total time of 9 hours. what is the speed of the wind?
2007-08-20 05:24:10 · 3 answers · asked by talonstrb 2 in Science & Mathematics ➔ Mathematics
The speed of a airplane in still air is 235 Km/h.the plane travels 498 Km/ against the wind and 1378 Km with the wind, in a total time of 9 hours. what is the speed of the wind? this is how it is worded in the text book tank you all for your help.i need all i can get.
2007-08-20 05:47:13 · update #1
I'm assuming the "/h" is a typo and you mean that the plane travels 498km (not "per hour") against the wind.
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Time = distance/rate. In this case there are two distances (498 and 1378) and two rates (235 less wind speed going into the wind, 235 plus wind speed with the wind). And the sum of the two times is 9 hours:
498 / (235 - w) + 1378 / (235 + w) = 9
Multiply by (235 - w)(235 + w) to get everything out of the denominators:
498 (235 + w) + 1378 (235 - w) = 9(235^2 - w^2)
117030 + 498w + 323830 - 1378w = 497025 - 9w^2
Combine like terms, and use the quadratic equation:
9w^2 - 880w - 56165 = 0
w = (- (-880) +/- sqrt((-880)^2 - 4*9*(-56165))) / (2*9)
w = ( 880 +/- sqrt(774400 + 2021940) ) / 18
w = (880 +/- 1672.23) / 18
Ignoring the negative answer, w = 141.8 km/hr.
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Checking the answer:
498 / (235 - 141.8) = 5.343 hours
1378 / (235 + 141.8) = 3.657 hours
5.343 + 3.657 = 9.000 to four digits accuracy.
2007-08-20 05:32:33 · answer #1 · answered by McFate 7 · 0⤊ 0⤋
Well, if the plane travels 1378km in 9 hours, that's
1378km/9h = 153.11 km/h.
Since it the plane travels faster into the wind than with the wind, I would assume that you have stated the problem backwards. But that shouldn't affect the solution.
The problem still doesn't make sense. If the plane travels at 235 km/hr, then the wind speed would be 235km/h - 498 km/h = -263 km/h. But if you calculate the wind speed from the speed with the wind, you get 235km/h - 153 km/h = 82 km/h.
So, there is really no way to solve this problem as written.
Perhaps, you mean to say that the plane travels 498km against the wind, not 498km/h. One is a distance and the other is a speed.
2007-08-20 12:35:08 · answer #2 · answered by Larry C 3 · 0⤊ 1⤋
Hey buddy... can u define the question more precisely... i hope the data is insufficient...
2007-08-20 12:40:53 · answer #3 · answered by Ollilu 1 · 0⤊ 2⤋