A plane encounters a tailwind and averages 289 mph.However on the return trip the plane now traveling against the same wind averages 257 mph.Find the speed of .

Question

I need help with my math homework and its due tomorrow.  Please help!

Answer 1

The question was cut off, but I think the following would provide the relevant answers.

Let’s start by calling x the normal air speed of the plane, without any wind effects.

Let’s call a the speed of the wind. When it is a tailwind, it adds to the normal speed, and when it is a headwind, it subtracts from the normal speed.

So, we have two equations:

1)  x + a = 289  Normal speed plus tailwind speed equals 289 mph

2)  x - a = 257  Normal speed minus headwind speed equals 257 mph

Step 1

Rearranging the first equation by subtracting a from both sides, we get  x = (289 - a)

Step 2

Substituting (289 - a) for x in the second equation, we get

(289 - a) - a = 257

Step 3

Simplifying and rearranging the second equation

 i)   289 - 2a = 257

 ii)  -2a = 257 - 289  (Subtract 289 from both sides)

 iii) -2a= -32

 iv)    2a= 32  (After multiplying each side by -1)

Therefore   a = 32/2

        a = 16

So, the wind speed, a is 16 miles per hour

Step 4

In order to find the normal speed, x, we add and/or subtract the wind speed, a, to the faster and slower speed of the plane

x = 289 - 16 = 273 (Subtracting the tailwind from the faster speed)

Or

x = 257 + 16 = 273 (Adding the tailwind speed to the slower speed)

So the normal speed of the aircraft without wind effects is 273 miles per hour. Voila!