Question

A plane can fly 260 miles downwind in the same amount of time as it can travel 170 miles upwind. Find the velocity of the wind if the plane can fly 215 mph in still air

Answer 1

by "miles" do you mean mph?

Answer 2

yes

Answer 3

no, it means in some amount of time T, the plane can fly 260 miles downwind, or 170 mile upwind. It doesn't necessarily mean that it is flying at 260 mph or 170 mph, unless 1 hour is the amount of time it takes to fly those legs.

Answer 4

"in the same amount of time" is the clue that you are talking about a distance, not a rate.

Answer 5

i figured it out thanks

Answer 6

What did you get for an answer?

Answer 7

from that information I don't believe you can ascertain a velocity of the wind.

Answer 8

Yes, you most certainly can.

Still air speed \(v_s = 215\)
Wind speed \(w\)
Downwind air speed \(v_d = v_s + w\)
Upwind air speed \(v_u = v_s - w\)
Flying for time T, we go 260 miles downwind, or 170 miles upwind
\(d=st\) or \(t = d/s\)
We know the two times are equal, so
\[\frac{260}{v_d} = \frac{170}{v_u}\]Cross multiply \[260v_u = 170v_d\]Now substitute in our other relations\[260(v_s-w) = 170(v_s+w)\]\[260v_s - 260w = 170v_s + 170w\]\[90v_s = 430w\]\[w = \frac{90v_s}{430} = \frac {90*215}{430} = 45\]

The wind speed is 45 mph.

Check our work: flying against the wind, our speed is 215 - 45 = 170. With the wind, our speed is 215 + 45 = 260. (both in mph). In 1 hour of flight upwind, we'll go 260 miles, and 1 hour of flight downwind we'll go 170 miles. That all matches the problem statement, so our answer is correct.

Answer 9

Note that the problem could have said "in an equal time, you fly 520 miles downwind and 340 miles upwind" and then you would not have the coincidence that the distances and the rates appear to be equal.

Answer 10

The answer, however, would be exactly the same.