Question
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.
Answers
GPT 3.5
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}.
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}.