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.
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}.
Let's assume the speed of the train is x miles per hour.
According to the given information, the train travels 160 miles in the same time as the plane covers 720 miles. Therefore, we can set up the following equation:
160 / x = 720 / (5x - 40)
To solve this equation, we can cross-multiply:
160(5x - 40) = 720x
Expanding the equation:
800x - 6400 = 720x
Now, subtract 720x from both sides of the equation:
800x - 720x = 6400
Combining like terms:
80x = 6400
Dividing both sides by 80:
x = 6400 / 80
Simplifying:
x = 80
So, the speed of the train is 80 miles per hour.
Now, let's find the speed of the plane. According to the given information, the speed of the plane is 40 miles per hour less than 5 times the speed of the train.
Speed of the plane = 5 * speed of the train - 40
= 5 * 80 - 40
= 400 - 40
= 360
Therefore, the speed of the plane is 360 miles per hour.
To solve this problem, we can use the formula:
Distance = Speed × Time
Let's first find the time it takes for both the train and the plane to cover their respective distances:
Let the speed of the train be x miles per hour.
Distance covered by the train = 160 miles
Time taken by the train = Distance/Speed = 160/x
Now, let's find the speed of the plane in terms of x:
Speed of the plane = 5 times the speed of the train - 40
Let the speed of the plane be y miles per hour.
y = 5x - 40
Distance covered by the plane = 720 miles
Time taken by the plane = Distance/Speed = 720/y
Since the train and the plane take the same time to cover their distances, we can set up the equation:
160/x = 720/y
Now, substituting y = 5x - 40 into the equation, we get:
160/x = 720/(5x - 40)
To solve for x, we can cross-multiply:
160(5x - 40) = 720(x)
800x - 6400 = 720x
Simplifying the equation:
800x - 720x = 6400
80x = 6400
x = 6400/80
x = 80
Now that we have the value of x, let's find the value of y using the equation y = 5x - 40:
y = 5(80) - 40
y = 400 - 40
y = 360
Therefore, the speed of the train is 80 miles per hour and the speed of the plane is 360 miles per hour.