The sum of the speeds of two trains is 720.5 miles per hour. If the speed of the first train is 7.5 mph faster than the second train, find the speeds of each.
If the slower has speed x, then
x + x+7.5 = 720.5
Now solve for x
To find the speeds of the two trains, we can set up a system of equations based on the given information. Let's denote the speed of the second train as x miles per hour.
According to the problem, the speed of the first train is 7.5 mph faster than the second train. So, the speed of the first train can be represented as (x + 7.5) mph.
The sum of the speeds of the two trains is given as 720.5 mph, so we can set up the equation:
(x) + (x + 7.5) = 720.5
Combining like terms, we get:
2x + 7.5 = 720.5
Now, let's solve for x:
2x + 7.5 - 7.5 = 720.5 - 7.5
2x = 713
Dividing both sides of the equation by 2, we have:
2x/2 = 713/2
x = 356.5
Therefore, the speed of the second train is 356.5 mph.
To find the speed of the first train, we can substitute the value of x back into the equation:
Speed of first train = x + 7.5 = 356.5 + 7.5 = 364
Therefore, the speed of the first train is 364 mph and the speed of the second train is 356.5 mph.