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A helicopter goes 270 miles with the wind in the same time it can go 180 miles against the wind. The wind speed is 6 miles/hour. Find the speed with no wind.

I would like to know step by step as to how to set it up and solve.
Thank you
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3 Answers

Hey Tisha -- here's a verbal approach ... +6mph and -6mph creates a 90-mile spread ...
12mph means 90mi ... 180mi needs 24mph ... 270mi would need 36mph
=> windless is in between at 30mph ... Best wishes, ma'am :)
This is a classic "rate times time equals distance" word problem. If I write that in letters: rt=d, where rate=r, time=t, and distance=d.
In this word problem, the rate is made up of two things: the speed of the helicopter (lets call that r) and the speed of the wind (which is 6mph). When the helicopter is traveling with the wind, it goes (r+6)mph and when it is traveling against the wind, the helicopter goes (r-6)mph.
OK, we know the helicopter goes 270miles with the wind, so let's set up this "rt=d" equation filling in the numbers we know:
OK, we also know the helicopter goes 180miles against the wind, so that "rt=d" equation looks like this:
In both of those equations, we know that t=t since in this word problem the times are the same, but we are not given the time. No worries, let's rewrite each of those equations equal to t:
(I just divided both sides by the (r +/- 6))
Since t=t, then:
  270 = 180
 (r+6)   (r-6)
Cross-multiply to get rid of the fractions:
Gather your "r" terms on one side and the numbers on the other side:
Divide both sides by 90:
Therefore, the speed of the helicopter is 30mph.
We need to use the formula d=rt to solve this problem: To solve for x we rearrange the formula:
Let x be the speed with no wind.
Let time with the wind be tw and time against be ta
To solve for X;
270/x+6=180/x-6  cross multiply
270x -1620 = 180x +1080
90x = 2700
x = 30mph with no wind