It takes an express train 1hr longer to travel 240km than it does for a small plane to travel the same distance. If the plane travels twice as fast as the train, how fast does the plane travel?
This is an ex., they lay out online but I'm confused about how they've laid out the equation.
I would've said:
(1/1)+(240/v)=(240/2v)
They've laid it out with the 1 hr on the other side. If the planes values are on one side & the trains equivalent value (+1hr time) are on the other side why would the 1 be on the side of the plane?
I hope my question makes sense, thanks as always :) <3
Let n be the speed of the train. Then the planes speed would be 2n. So, you have:
240/n=(240/2n) +1
Then, solve for n
☺☺☺☺
but why is the +1 on the planes side of the equation when it was the train that took an hr longer?
Thanks again :)
Here is the way I used to explain this concept to my students when I was teaching a "long time ago".
You did agree that
the time for the train was greater than the time of the plane by 1, or
240/n > 240/2n by 1
right now the left side is greater than the right side by 1
How do i make them equal ?
by adding 1 to the smaller side, that is
240/n = 240/2n + 1
That makes total sense, thank you very much :)
Plane takes T hours.
Train takes T+1 hours.
Velocity of train = V km/h.
Velocity of plane = 2V km/h.
Plane: 2V*T = 240 km.
Train: V*T = 240 km.
Therefore, 2V*T = V*(T+1).
T = 1 h.
T+1 = 1 + 1 = 2 h.
2V*T = 240.
2V * 1 = 240,
2V = 240 km/h = Velocity of the plane.
To find the speed of the plane, we can start by setting up equations based on the given information.
Let's assume the speed of the train is 'x' km/h. According to the problem, the plane travels twice as fast as the train, so its speed will be '2x' km/h.
We are also given that the train takes 1 hour longer than the plane to travel a distance of 240 km.
The time taken by the train to cover 240 km can be calculated using the formula: time = distance/speed. So, for the train, the time will be 240/x hours.
Similarly, the time taken by the plane to cover the same distance is 240/(2x) hours.
According to the problem, the train takes 1 hour longer than the plane to cover the distance of 240 km. So, we can set up the equation:
240/x = 240/(2x) + 1
Now, let's solve this equation to find the speed of the plane:
Multiply both sides of the equation by 'x(2x)' to eliminate the denominators:
240(2x) = 240x + x(2x)
480x = 240x + 2x^2
Rearrange the equation in standard form:
2x^2 + 240x - 480x = 0
2x^2 - 240x = 0
Divide the entire equation by 2 to simplify:
x^2 - 120x = 0
Factor out an 'x':
x(x - 120) = 0
Now, we have two possible solutions:
x = 0 (which doesn't make sense in this context)
or
x - 120 = 0
Solving for x, we find:
x = 120
Since 'x' represents the speed of the train, we conclude that the train travels at a speed of 120 km/h.
As the problem stated, the plane travels twice as fast as the train, so the speed of the plane is:
2x = 2 * 120 = 240 km/h.
Therefore, the plane travels at a speed of 240 km/h.