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.

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