If a plane can travel 460 miles per hour with the wind and 400 miles per hour against the wind find the speed of the plane without a wind and the speed of the wind.

Question

anonymous · Answer

v + wind = 460
v - wind = 400

anonymous · Answer

Okay to get the answer I would have to subtract the 460 first or divide it?

anonymous · Answer

To get the answer you have to solve for one variable in terms of the other, and plug into the second equation, or add the two equations to cancel out one variable....
So for the lower equation rearrange it...
$$v - wind = 400$$ can be rewritten as $$v = 400 + wind$$ now plug this expression of v into the top equation!

anonymous · Answer

Still a bit confusing

anonymous · Answer

Do you understand how I have rewritten it?

anonymous · Answer

Yes

anonymous · Answer

ok, so you want to plug this into the other equation where v is... $$v + wind = 460$$
$$(400 + wind) + wind = 460$$ $$2wind + 400 = 460$$ $$2wind = 60$$ $$wind = \frac{ 60 }{ 2 } = 30$$

anonymous · Answer

Okay got it.

anonymous · Answer

Solve the following two equaitons for s and w, the speed of the plane and the wind respectively: $$\{s+w=460,s-w=400\} $$$$\{s=430,w=30\} $$