Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Lets say someone is flying at constant speed from place $X$ to place $Y$ and back. Going to X takes 5 hours (with the wind) and coming back from X to Y takes 6 hours. Lets assume that the wind is at a constant speed, then how long would it take for a piece of paper being propelled by the wind alone to travel from $X$ to $Y$.

share|cite|improve this question
Your $X$'s and $Y$'s are a little switched up... – process91 Aug 25 '12 at 12:49
whatis wrong? with them,? – fosho Aug 25 '12 at 12:49
It seems like the wind is blowing from $Y$ to $X$ in your second sentence, but your last sentence implies the opposite... luckily it is obvious what the question is looking for. – process91 Aug 25 '12 at 12:50
Read the middle part of your second line, @Daniel, to understand what Michael means... – DonAntonio Aug 25 '12 at 12:51
meant to read from Y to X sorry – fosho Aug 25 '12 at 12:53
up vote 3 down vote accepted

Heh, this problem is cute!

Suppose our (constant) speed is $v$, the (constant) speed of the wind is $w$, the time it takes for us to get from $Y$ to $X$ is $t_1$ and going back takes $t_2$. If the distance between $X$ and $Y$ is $d$, then because the speeds are all constant, we know $$ (v+w)t_1 = d = (v-w)t_2,$$ where the plus vs. the minus sign is because the faster direction ($Y$ to $X$) is where we're travelling in the direction of the wind. Putting the times in, we get $$ 5v + 5w = 6v - 6w,$$ and so $w = v/11$.

Now, the distance the piece of paper has to travel is that same as the distance we travel, so we have $$ t_1(v+w) = 5(v+w) = d = wt,$$ where $t$ is the amount of time the piece of paper takes to travel. Solving for $t$, we get $$ t = \frac{5(v + v/11)}{v/11} = \frac{5(12v/11)}{v/11} = 5\cdot 12 = 60.$$ So the piece of paper takes 60 hours to get from $Y$ to $X$.

share|cite|improve this answer

Let $\,v=\,$ someone's constant speed, and let $\,x=\,$ wind's constant speed from X to Y . If $\,d=\,$ distance between X and Y, we get (using the basic formula $\,v=d/t\,$) $$t=5=\frac{d}{v+x}\,\,\,,\,\,\,6=\frac{d}{v-x}\Longrightarrow 5v+5x=6v-6x\Longrightarrow v=11x\Longrightarrow$$ $$\Longrightarrow5=\frac{d}{12x}\Longrightarrow x=\frac{d}{60}$$

Thus, a paper fying from X to Y without dragging and gliding will make the distance in $$t=\frac{d}{x}=60\,\,\text{ hours}$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.