# Using Linear To Solve Problem

1. Dec 4, 2009

### yuuri14

1. The problem statement, all variables and given/known data
At maximum speed, an airplane travels 2400 miles against the wind in 6hrs. Flying with the wind, the plane can travel the same distance in 5hrs.
Let x be the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind.

2. Relevant equations
well first of all, I need to come up with an equation of inequality or linear for this problem.

3. The attempt at a solution
x= max speed
y=speed of the plane
known:2400m/6hrs against wind
2400m/5hrs with wind

can someone give a hint of an equation to approach this problem?

2. Dec 4, 2009

### Staff: Mentor

y is not the speed of the plane, it is the speed of the wind.

The max speed of the plane is x, which is when the plane's inherent speed (call it v) is added to the speed of the wind [STRIKE](call it w)[/STRIKE] (call it y). Now the one constant thing you have in this problem is the distance that is flown (it's the same both ways, right?) -- call that d.

So write the two equations for how long it takes to travel the distance d, one with the tail wind in the shorter time, and one with the headwind in the longer time.

Last edited: Dec 4, 2009
3. Dec 4, 2009

### yuuri14

So would it rate x time= distance
6(x-y)=2400 against the wind
5(x+y)=2400 with the wind

6x-6y=2400
x-y=400
y=400-x
-------------------------
5x+5y=2400
x+y=480
x-(400-x)=480
2x-400=480
2x=880
x=440
---------------------------
6(x-y)=2400
6(480-y)=2400
2880+2y=2400
2y=-480
y=-240
is this wrong I ended up w/ a (-) number

4. Dec 4, 2009

### Staff: Mentor

Re-check this step. You were correct up to that point. Good job!

5. Dec 4, 2009

### yuuri14

opps my mistake.
6(x-y)=2400
6(480-y)=2400
2880-6y=2400
-6y=-480
y=80
is this right. So is this the answer if their no wind for the plane or is there another step to it?

6. Dec 4, 2009

### Staff: Mentor

x is not 480. Double check what you got above when you solved for x.

And x is the max speed of the plane, right? And y is the speed of the wind. So what is the speed of the plane with no wind?

7. Dec 4, 2009

### yuuri14

6(x-y)=2400
6(440-y)=2400
2640-6y=2400
-6y=-240
y=40

well i know that:
x is the max speed of the plane :440
y is the speed of the wind:40
if i divide it its: 11.......is that the answer???

8. Dec 4, 2009

### Staff: Mentor

Don't divide. Don't guess.

If you have an airspeed of 100mph, and a 10mph tailwind, what is your groundspeed? Think about it...

9. Dec 4, 2009

### yuuri14

why do i have to use 100mph, and a 10mph tailwind? It wasn't given to the original problem.