Question

Which set of equations would be used to solve this word problem?

An airplane flew 5 hours with a 50 mph head wind. The return trip with a tail wind of the same speed took 3 hours. Find the speed of the plane in still air.

d = 8(r + 50)

d = 5(r + 50) and d = 3(r − 50)

d = 5(r − 50) and d = 3(r + 50)

None of these systems can be used to solve this problem.

Answer 1

@Directrix

Answer 2

These are always tricky so let's think a moment.

Answer 3

Ok

Answer 4

I'm thinking about the d = r*t formula. (distance = rate times time) and how to set it up.

Answer 5

The distance formula is d = rt, where d represents distance, r represents rate, and t represents time.

Answer 6

Thats what i have from my notes

Answer 7

Do you think a head wind slows the plane and a tail wind speeds the plane or the other way around? @HelloGoodmorning

Answer 8

I think its this way around

Answer 9

So, the head wind slows the plane, and the tail wind speeds the plane.

Answer 10

The distance both ways on the trip are the same. You agree @HelloGoodmorning

Answer 11

Yes

Answer 12

Variables:
d is distance
r is rate of speed in still air
t is time


Trip out:
d is distance
(r - 50) is rate of speed with head wind
t = 5 hrs.

Trip back:
d is distance
(r + 50) is rate of speed with tail wind
t = 3 hours

@HelloGoodmorning Do you agree with these variable assignments?

Answer 13

Yes I do I see the method that you're using as wel

Answer 14

But does that mean we found our answer

Answer 15

@Directrix

Answer 16

No, that is not the answer. That is part of the process.

Answer 17

Oh okay.

Answer 18

Trip out:

d = (r - 50)*5

Trip back:

d = (r + 50)*3


@HelloGoodmorning What is the question? We need to know what to do with these two equations.

Answer 19

I think I see the correct option. Do you? @HelloGoodmorning

Answer 20

No not really give me a second to re look over it

Answer 21

@Directrix

Answer 22

You are looking for something equivalent to:

d = (r - 50)*5
d = (r + 50)*3 @HelloGoodmorning

Answer 23

Yes i do see the answer it's b @Directrix

Answer 24

No. Look again. You have to look at every number. It's a little tricky but you can do it. @HelloGoodmorning

Answer 25

ok :( lets try again

Answer 26

Option B has this in it: d = 5(r + 50)

and our work did not. That is why B is not the correct option.

Answer 27

oh it's d

Answer 28

No.

Answer 29

no?

Answer 30

not d sorry c

Answer 31

looked at it too fast

Answer 32

@Directrix

Answer 33

What might have thrown you off is the the option looks like this:

d = 5(r − 50) and d = 3(r + 50)

Ours looked like this: d = (r - 50)*5 d = (r + 50)*3

The commutative property says that they are the same. So, Option C is the one.

Answer 34

Yes it did lol thanks very much @Directrix

Answer 35

You are welcome.