the speed of train A is 8mph slower than the speed of train B. Train A travels 220 in the same time it takes train B to travel 260 miles. Find the speed for each train.
To find the speeds of the two trains, we can set up a system of equations based on the given information.
Let's assume the speed of train B is "x" mph.
According to the problem, the speed of train A is 8 mph slower than train B, so the speed of train A is (x - 8) mph.
Now let's set up the equation based on the time it takes for each train to travel their respective distances.
The time taken by train B to travel 260 miles is given as t (let's assume t hours).
Therefore, the time taken by train A to travel 220 miles will also be t hours.
We can use the formula Speed = Distance / Time to create equations for each train:
Equation 1:
Speed of train A = Distance traveled by train A / Time taken by train A
(x - 8) = 220 / t
Equation 2:
Speed of train B = Distance traveled by train B / Time taken by train B
x = 260 / t
Now we have a system of equations:
(x - 8) = 220 / t
x = 260 / t
To solve this system, we can eliminate the "t" variable by setting the two right sides of the equations equal to each other:
220 / t = 260 / t
To remove the denominator, we can cross multiply:
220 * t = 260 * t
Divide both sides by t:
220 = 260
This equation is not true, which means there is no solution. Therefore, there is no consistent speed for train B, and train A cannot be 8 mph slower than an undefined value.
Thus, there is no valid solution for the speed of each train using the given information.
solve
220/x = 260/(x+8)
Hint: cross-multiply