Question

a plane traveled 3246 miles with the wind in 6 hours, and 2814 miles against the wind in the same time. Find the speed of the plane and the wind

Answer 1

Divide to find the two speeds.

Answer 2

Then you'll have plane + wind for one and plane - wind for the other.

Answer 3

Those will be your two equations to solve for the two unknowns.

Answer 4

that really didnt help.

Answer 5

Have you done any similar problems before?

Answer 6

no

Answer 7

What don't you understand about what I told you to do?

Answer 8

you were vague

Answer 9

i onyl have 4 minutes can someone pleqsae help me

Answer 10

\[\frac{ 3246 }{ 6 }=v_p+v_w\]
\[\frac{ 2814 }{ 6 }=v_p-v_w\]

Answer 11

I'm vague because I want you to do some thinking on your own, @strcaitlyn13 .
I have respect for your intelligence and don't want to insult you by telling you things you already know.

Answer 12

3246/(p+w) =6
2184/(p-w) =6
p+w=3246/6
p-w=2184/6
solve for p and w
p+w=541
p-w=364
add
2p=905
p=905/2
subtract
2w=177
w=177/2

Answer 13

And then there's always that helpful soul who will insult your intelligence and betray the sanctity of the learning process (*cough* code of conduct *cough*) by merely giving you the solution.
Oh well, not everyone wants to actually be educated.

Answer 14

so is it 88.5? and 354

Answer 15

452.5,88.5

Answer 16

Ah, all that work, and your solutions are incorrect, @gomathi ...

Answer 17

Here's a hint: The solutions are whole numbers.

Answer 18

One of the advantages of math, is the ability to verify your answers or "checking" them.
In this case, let us verify the answer 452.5 mph for the airplane speed and 88.5 mph for the wind speed. when the plane was flying with the wind, the combined speed using d=rt,
3246=r6, thus rate is 3246/r or 541 mph now for check: 452.5 + 88.5 = 541.0 that checks out.

Answer 19

When the plane is flying against the wind, you can also verify those values.

Answer 20

Uh huh, and do those check out?

Answer 21

They do indeed.

Answer 22

Really?

"a plane traveled 3246 miles with the wind in 6 hours, and 2814 miles against the wind in the same time. Find the speed of the plane and the wind"

Answer 23

As show in my post the combined rate (mph) when traveling with the wind would be
3246/6 or a rate of 541 mph. This is the result of the airplane's speed plus the wind speed. or plane + wind = 541 mph.
In a similar manner calculate the combined rate when flying in opposition to the wind (against the wind) that would be 2814/6 = 469 mph. This is the airplane speed minus the wind speed.
let A = airplane speed and
let W = wind speed
A+W=541 mph
A-W=469 mph using elimination method
2A = 1 0 1 0
A= 505 New "corrected" speed if plane is now 505 mph (lol)
W=541-505 =36 mph a more reasonable wind speed !
I see where the value of 2184 was used instead of 2814 resulting in an error.
Good catch Cliffsedge.

Answer 24

I wouldn't want to fly in hurricane force winds either.