Finding the speed of the wind and an airplane in still air

[mariasalto32]

Flying against the wind, an airplane travels
3420km
in
6
hours. Flying with the wind, the same plane travels
2670km
in
3
hours. What is the rate of the plane in still air and what is the rate of the wind?

 

[MarkFL]

Hello and welcome to MHB! :)

In order to really be able to help you we need to see what you have tried so we know where you are stuck or what you may be doing wrong. Having said that, I would begin by defining variables to represent the two unknown quantities we are asked to find. We could let $p$ be the speed of the plane in still air, and $w$ be the speed of the wind. These speeds will be in kilometers per hour. Using the relationship between distance $d$, constant speed $v$ and time $t$:

$$d=vt$$

we may then state using the given information:

$$3420=(p-w)6$$

$$2670=(p+w)3$$

If we divide the first equation by 6 and the second by 3, we obtain the simpler system:

$$570=p-w$$

$$890=p+w$$

Now, you can add these two equations together to eliminate $w$ and solve for $p$, and then use this value of $p$ and either of these two equations to find $w$. What do you get?

 

[MarkFL]

Re: word problem please help

Adding the two equations, we obtain:

$$1460=2p\implies p=730$$

Now, using the first of the two equations we added and the value of $p$, we have:

$$570=730-w\implies w=10(73-57)=160$$

And so we have found the speed of the plane in still air is 730 kph, and the speed of the wind is 160 kph.