Answer: 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.
