Flying with a tailwind, a pilot flew an airplane 700 miles in 3.5 hours. flying into a headwind, the return trip took 5 hours. find the speed of the plane in calm air and the speed of the wind.

170 mph and 30 mph

Step-by-step explanation: Let's start things off by setting up variables based on the formula rate x time = distance for the 2 trips that the plane took into a headwind and with a tailwind.

If we use the variable p to represent the speed of the plane and w to represent the speed of the wind,

then we can represent the speed of the plane into a headwind as p - w and the speed of the plane with a tailwind as p + w.

The time of the headwind trip is 5 hours and the time for the tailwind trip is 3.5 hours so based on our formula rate x time = distance, the distance for our headwind trip is 5(p - w) and the distance for our tailwind trip is 3.5(p + w).

Since we know the actual distance that the plane flies in each direction is 700 miles, we can set each of our 2 distances equal to 700.

So we have 5(p - w) = 700 and 3.5(p + w) = 700. As our next step, I would divide both sides of our first equation by 5 to get p - w = 140 and divide both sides of the second equation by 3.5 to get p + w = 200.

p - w = 140

p + w = 200

When we add these 2 equations together,

the w's cancel and we have 2p = 340.

Divide both sides by 2 and p = 170.

To find w, substitute p back into either equation and

we find that w = 30.

So the speed of the plane is 170 mph and

the speed of the wind is 30 mph.

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

step-by-step explanation: