Another word problem, please help??

Question

A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane's speed in still air?

Answer 1

it doesnt have any time in still air - it is always going against the wind or being wind assisted

Answer 2

150 mi/h

To turn it into an algebra problem, you need to find the speed the plane would fly if there were no wind. It takes:

720 mi/(x-30) hours to fly there against the wind and
720 mi/(x+30) hours to fly back with the wind
The total flight time is 10 hours so,

720/(x-30) + 720/(x+30) = 10

Create a common denominator on the left to get

720(x-30) + 720(x+30)
----------------------------------- = 10
(x-30)(x+30)

Multiply out and group to get

1440x
--------------- = 10
x^2 - 900

Move denominator over to get

1440x = 10x^2 - 9000

Bring everything together for something factorable

10x^2 - 1440x - 9000 = 0

Divide everything by 10 to make it easier to eyeball the factors

x^2 - 144x - 900 = 0

The factors are 150 and 6 (150*6 = 900, 150-6=144)

Since 6 is clearly a nonsensical answer in the context of the question, plug in 150 to check

720/180 = 4, 720/120 = 6, 4+6 = 10

Note that a tempting solution, 720*2/10 = 144mi/hr is the plane's average speed, not its speed in still air.

Answer 3

Let Sally work x hours per week therefore karl works x+4 hours per week the equation is 6x=3(x+4) 6x-3x=12 3x=12 x=4 Karl works x+4 hours a week so, Karl works 8(4+4) hours a week.

Answer 4

Total distance traveled 1440 miles divided by 10 hours = 144mi/hr.

Answer 5

dear friend
wow, r U scientist?

well i dont take tensions. whatever things are. make life simpler rather making it complicated.
if you are in the plane just enjoy the air trip.

hve gr8 day
raj

Answer 6

Like your other one, this is not a word problem. It's a mathematical problem.