Train A has a speed 15 miles per hour greater than that of train B. If train A travels 240 miles in the same times train B travels 180 miles, what are the speeds of the two trains?
since time = distance/speed, If B has speed x, then
240/(x+15) = 180/x
240x = 180(x+15)
4x = 3(x+15)
x = 45
B goes 45, A goes 60
check:
240/60 = 180/45 = 4
Let's assume the speed of Train B is "x" miles per hour.
According to the given information, the speed of Train A is 15 miles per hour greater than that of Train B. Therefore, the speed of Train A can be stated as "x + 15" miles per hour.
Now, let's calculate the time taken by Train B to travel 180 miles. We can use the formula:
Time = Distance / Speed
So, the time taken by Train B is 180 / x hours.
Similarly, we can calculate the time taken by Train A to travel 240 miles:
Time = Distance / Speed
The time taken by Train A is 240 / (x + 15) hours.
Since both trains travel the same time, we can set up an equation as:
180 / x = 240 / (x + 15)
To solve this equation, we can cross multiply:
180(x + 15) = 240x
180x + 2700 = 240x
2700 = 240x - 180x
2700 = 60x
Divide both sides of the equation by 60:
2700 / 60 = x
x = 45
Therefore, the speed of Train B is 45 miles per hour.
To find the speed of Train A, we can substitute the value of x back into the equation:
Speed of Train A = x + 15 = 45 + 15 = 60 miles per hour.
Hence, the speeds of the two trains are 45 miles per hour for Train B and 60 miles per hour for Train A.
To find the speeds of the two trains, we can set up a system of equations based on the given information.
Let's assume that the speed of Train B is x miles per hour. Therefore, the speed of Train A is x + 15 miles per hour (since Train A is 15 miles per hour faster than Train B).
Using the formula speed = distance / time, we can write the following equations:
For Train A: speed_A = (240 miles) / t hours
For Train B: speed_B = (180 miles) / t hours
Since both trains take the same time to travel their respective distances, we can set these two equations equal to each other:
speed_A = speed_B
(240 miles) / t = (180 miles) / t
Now we can solve for t by cross-multiplication:
240 miles * t = 180 miles * t
240t = 180t
Subtract 180t from both sides:
240t - 180t = 180t - 180t
60t = 0
Divide both sides by 60:
60t / 60 = 0 / 60
t = 0
However, we know that time cannot be zero, so this means that the equation does not have a valid solution for time. This implies that there is an error in the given problem.
Without a valid time value, we cannot calculate the speeds of the two trains.