Two trains travel for eleven hours, starting from the Same place traveling in opposite directions. One train travels at an average rate that is 15 mph faster than the other train. Find the rate of each train if they are 291 miles apart after three hours
Let's assume the rate of the slower train is x mph.
The rate of the faster train is x + 15 mph.
In 3 hours, the slower train would have traveled a distance of 3x miles.
In 3 hours, the faster train would have traveled a distance of 3(x + 15) miles.
The total distance between the trains after 3 hours is 291 miles. Therefore, we can write the equation:
3x + 3(x + 15) = 291
Simplifying the equation:
3x + 3x + 45 = 291
6x + 45 = 291
6x = 291 - 45
6x = 246
x = 246/6
x = 41
So, the rate of the slower train is 41 mph, and the rate of the faster train is 41 + 15 = 56 mph.
To find the rates of each train, we can use a system of equations. Let's denote the rate of one train as x mph, and the rate of the other train as (x + 15) mph.
Since both trains travel for 11 hours, we can use the formula Distance = Rate * Time to calculate the distance each train has traveled.
For the first train, its distance traveled is x mph * 11 hours = 11x miles.
For the second train, its distance traveled is (x + 15) mph * 11 hours = 11(x + 15) miles.
Since the two trains are traveling in opposite directions, the sum of their distances should be equal to the total distance between them, which is 291 miles.
Therefore, we can set up the equation:
11x + 11(x + 15) = 291
Simplifying the equation:
11x + 11x + 165 = 291
22x = 291 - 165
22x = 126
x = 126 / 22
x ≈ 5.73
So, the rate of the first train is approximately 5.73 mph, and the rate of the second train is approximately 5.73 + 15 = 20.73 mph.
If the slower train has speed x, then since distance = speed * time,
3(x + x+15) = 291
Solve for x, then get x+15