A small jet can fly 1008 miles in

4 hours with a tailwind but only 832 miles in 4 hours into a headwind. Find the speed of the jet in still air.

Well, talking about jets, I once tried fitting into one of those tiny airplane bathrooms. Let's just say the experience was more like being in a clown car. But let's get to the question at hand.

To find the speed of the jet in still air, we'll use a little math, but don't worry, I won't make it as complicated as trying to do calculus on a unicycle.

Let's call the speed of the jet in still air "x" and the speed of the wind "y." When the jet has a tailwind, its speed is increased by the speed of the wind, so we can say its effective speed is (x + y). Likewise, when it's flying against a headwind, its effective speed becomes (x - y).

Now, according to the problem, the jet can fly 1008 miles in 4 hours with a tailwind, so we can set up the equation:
4(x + y) = 1008
Now, when the jet is flying into a headwind, it can only cover 832 miles in 4 hours:
4(x - y) = 832

Now, let's solve this mystery called math and find the value of x, the speed of the jet in still air.

After some number crunching, I can reveal that the speed of the jet in still air is 160 mph. And let's just hope there are no clowns flying it.

Let's assume the speed of the jet in still air as 'x' miles per hour.

Let the speed of the wind be 'w' miles per hour.

When the jet is flying with the tailwind, its effective speed is increased by the speed of the wind. Thus, the speed of the jet with a tailwind is (x + w) miles per hour.

According to the given information:
The distance covered by the jet with a tailwind in 4 hours is 1008 miles.
So, the speed of the jet with a tailwind is 1008/4 = 252 miles per hour.

Using the equation (x + w) = 252, we have the first equation: x + w = 252.

Similarly, when the jet is flying into a headwind, its effective speed is decreased by the speed of the wind. Thus, the speed of the jet against the wind is (x - w) miles per hour.

According to the given information:
The distance covered by the jet against the wind in 4 hours is 832 miles.
So, the speed of the jet against the wind is 832/4 = 208 miles per hour.

Using the equation (x - w) = 208, we have the second equation: x - w = 208.

Now, let's solve these two equations to find the values of 'x' and 'w', which will give us the speed of the jet in still air.

Adding the two equations together, we get:
(x + w) + (x - w) = 252 + 208,
2x = 460,
x = 460/2,
x = 230.

Therefore, the speed of the jet in still air is 230 miles per hour.

To find the speed of the jet in still air, we can use the concept of relative velocity.

Let's assume the speed of the jet in still air is v mph.

With a tailwind, the jet can cover 1008 miles in 4 hours. Since the tailwind helps to increase the speed of the jet, we need to add the speed of the tailwind to the speed of the jet in still air.

The formula for distance is speed multiplied by time, so distance = speed × time.

With a tailwind, the effective speed of the jet is (v + w) mph, where w is the speed of the tailwind.

Using the formula distance = speed × time, we can write the equation for the distance covered with a tailwind as:
1008 = (v + w) × 4

Similarly, when the jet is flying into a headwind, the effective speed is reduced by the speed of the headwind. So, the effective speed is (v - w) mph.

Using the formula distance = speed × time, we can write the equation for the distance covered into a headwind as:
832 = (v - w) × 4

Now, we can solve this system of equations to find the values of v and w.

Dividing the first equation by 4, we have:
252 = v + w

Dividing the second equation by 4, we have:
208 = v - w

Adding these two equations together eliminates the variable w, and we get:
252 + 208 = 2v

Simplifying, we get:
460 = 2v

Dividing by 2, we find:
v = 230

Therefore, the speed of the jet in still air is 230 mph.

speed of jet in still air ---- x mph

speed of wind ---- y mph

4(x+y) = 1008 ---> x+y = 252
4(x-y) = 832 ----> x-y = 208

add them: 2x = 460
x = 230

from x+y = 252 , y = 22