A train travels 160 miles in the same time that a plane covers 720 miles. If the speed of the plane is 40 miles per hour less than 5 times the speed of the​ train, find both speeds.

Answer 1

Let's suppose the speed of the train is "x" miles per hour.
Then, the speed of the plane is (5x-40) miles per hour.
We know that time is equal to distance divided by speed.
So, the time it takes for the train to travel 160 miles is 160/x.
And the time it takes for the plane to travel 720 miles is 720/(5x-40).
Since both times are equal, we can set up the equation:
160/x = 720/(5x-40).
Now, let's cross-multiply:
160(5x-40) = 720(x).
800x - 6400 = 720x.
800x - 720x = 6400.
80x = 6400.
x = 6400/80.
x = <<80=80>>80.
So, the speed of the train is 80 miles per hour.
Therefore, the speed of the plane is 5*80 - 40 = <<5*80-40=400-40=360>>360 miles per hour. Answer: \boxed{80, 360}.