An airplane travels 600 miles against the wind in 4 hours, and makes the return trip with the same wind in 2 hours. Find the rate

Question

whpalmer4 · Answer

I love these problems :-)

Okay, the plane flying with the wind goes at a speed of $s+w$ over the ground, where $s$ is the speed of the plane without any wind, and $w$ is the speed of the wind.

The plane flying against the wind goes at a speed of $s-w$ over the ground.

Using the distance formula $d = s * t$ where $d$ is distance, $s$ is speed, and $t$ is time, we have two equations:

$$600 = (s-w)*4\text{            (flying against the wind)}$$$$600 = (s+w)*2\text{            (flying with the wind)}$$
Do you know how to solve that system of equations?

anonymous · Answer

will I add s and w together?

whpalmer4 · Answer

Distribute the stuff on the right hand sides first.  What do you get for the two equations?

whpalmer4 · Answer

$$600 = 4s - 4w$$$$600=2s+2w$$

anonymous · Answer

6s-2w=600

whpalmer4 · Answer

Uh, no, that isn't what we want.  We need to multiply one or both of the equations by numbers that will make one of the columns of coefficients have equal values with opposite signs, perhaps $-4w$ and $4w$.  Then when we add the two equations together, that variable will vanish and we'll have a new equation in only one variable to solve.

whpalmer4 · Answer

What happens if you multiply the second equation by 2?

whpalmer4 · Answer

$$600=4s-4w$$$$2*600 = 2*2s + 2*2w$$

$$600=4s-4w$$$$1200=4s+4w$$-----------------
$$600+1200= 4s+4s -4w + 4w$$$$1800=8s+0w$$$$s=$$

whpalmer4 · Answer

From the value you get for $s$, you can find $w$ by plugging the value of $s$ into either of the equations and solving for $w$.

anonymous · Answer

divide 1800 by 8? Cancel out the 0

whpalmer4 · Answer

so the value of $s$ is?

whpalmer4 · Answer

Hey, you're not done yet.  You need to find the value of $w$, then check your work by plugging the values you found for $s$ and $w$ into both equations to make sure that both are satisfied.